An African grey parrot costs ~$2k/parrot. For a small breeding population might be ~150 individuals (fox domestication started out "with 30 male foxes and 100 vixens"). Let's assume cages cost $1k/parrot, including perches, feeding- and water-bowls. The estimated price for an avian vet is $400/parrot-year.

This page also says that African greys produce feather dust, and one therefore needs airfilters (which are advisable anyway). Let's say we need one for every 10 parrots, costing $500 each.

Let's say the whole experiment takes 50 years, which is ~7 generations. I'll assume that the number of parrots is not fluctuating due to breeding them at a constant rate.

Let's say it takes $500/parrot for feed and water (just a guess, I haven't looked this up).

We also have to buy a building to house the parrots in. 2m²/parrot at $100/m² in rural areas, plus $200k for a building housing 50 parrots each (I've guessed those numbers). Four staff perhaps (working 8 hours/day), expense at $60/staff-hour, 360 days a year.

The total cost is then 150*$2k+15*$500+150*$1k+150*50*($400+$500)+3*$200k+2*150*$100+50*360*8*4*$60=$3.632 mio.

I assume the number is going to be very similar for other (potentially more intelligent) birds like keas.

The smartest parrots (by Michael Woodley's website) are the kea and the greater vasa parrot (he found cockatoos to be "middling" on the string-pulling task, but cockatoos seem to be more "generalist" than even african greys and seem better at tool-using). Figuring out genetic phylogeny of the "smarter parrots" vs "dumber parrots" (we've made some similar papers+YouTube videos for comparing regions of accelerated evolution in human genes vs chimpanzee brains, though the power would probably be lower since it's not super-clear which parrots are smarter)

Kea are smart enough to use touchscreens and easy enough to breed - there is a way to measure their "g-factor", as Michael Woodley is trying to do. He is also in contact with the Vienna kea lab where they do research on individual differences in kea problem-solving

[Michael Woodley believes that there is a g-factor to birds, with corvids having unusually high g-factors. I don't know if he has used the g-factor to all broad metrics, including ones that go beyond string-pulling]

What about, just culturing parrot iPSC cells into neurons? (where their growth might not be limited by the small size of the birdbrain skill). Like those of the kea? Michael Woodley purchased a kea from a Spanish breeder - moreover - there are conservation+Geochurch-based reasons to culture/better understand iPSC neurons of endangered birds (aka these papers [just by culturing iPSC neurons alone] would be publishable for many reasons even if you couldn't get the neurons to do "interesting things") + organoids make it easier for us to do less animal testing

[Michael Woodley  - now figure out their individual differences and genotype+do "all the metabolomic/transcriptomic+MRI" analysis on the individual kea (John Marzuff has put wild crows in MRIs) and put them in a kea biobank just as we have sequences the genomes of all remaining kakapo].

[Kea are also going through a population bottleneck due to their high death rates, though some have recently learned to breed on trees rather than on the ground and some have learned to use sticks to bait stout-traps - these may improve selection for intelligence in kea on some timescale - their small population size bottleneck may affect their rate of brain evolution in some way, depending on how much genetic variation there is in theremaining populations of kea]. Kea are SUCH a weird bird that their inherently high entropy causes them to have high death rates - but they are sufficiently easy enough to breed in zoos that complete extinction seems unlikely + some seem sufficiently resourceful enough to stay out of death-causing levels of trouble, despite their population that is still decreasing/bottleneck'ing (possibly due to mammalian predation on their young, which is fixable given that they can adapt to breeding above ground)

There is also so little research in the brain architecture of parrots (I know Suzana Herculano-Houzel  has done some, but neuron density is not enough when connectonomics is cheaper than before) that we still don't know electrophysiological or synaptic connectivity properties vary from species to species [birds being much smaller makes the problem much more tractable than doing it for many marine mammals]

[related -https://www.anl.gov/article/contrary-to-expectations-study-finds-primate-neurons-have-fewer-synapses-than-mice-in-visual-cortex, https://www.genengnews.com/news/ion-channel-density-surprisingly-different-for-human-neurons/ ]

[also figure out what percent of brain of the more resourceful parrots is devoted to the pallium]

[redo the analysis on accelerated human regions

 for parrot brains]

https://www.sciencedaily.com/releases/2021/09/210902124922.htm

https://zuckermaninstitute.columbia.edu/finding-brainy-genes-make-us-human

[https://www.nature.com/articles/s41598-022-12953-4]

https://www.researchgate.net/publication/227464305_Rethinking_birdsong_evolution_Meta-analysis_of_the_relationship_between_song_complexity_and_reproductive_success

You do not need to change that many genes in order to induce island giganticism to a species, and while bigger brains are not necessarily smarter brains between lineages (ungulates have much larger brains than dog-like carnivores, but don't appear any smarter, probably because their neuron architecture is less efficient), WITHIN LINEAGES, brain size can matter (bigger dogs do appear to be smarter dogs - https://www.aaha.org/publications/newstat/articles/2019-02/are-big-dogs-smarter-than-small-dogs/ ). 

Other relevant references:

https://www.quora.com/Which-bird-has-the-biggest-brain/answer/Alex-K-Chen

https://www.lesswrong.com/posts/eYFscbv5BJ8Fezauj/?commentId=LsgiACyug9AA6WL5e

It is argued here that a difference in neuronal density scaling is what differentiates primates from other mammals and is thus why large animals such  as elephants and whales are not more intelligent than humans despite their larger brains. Small mutations which affect neuronal density could thus lead to different humans having significantly different neuron counts (and hence scaling law IQs) despite having approximately the same gross brain volume.

(the scaling for parrots could be even better, but we just don't know yet. Worth investigating, given the stakes)

https://www.theguardian.com/science/2021/mar/24/scientists-discover-why-the-human-brain-is-so-big

https://www.sciencedirect.com/science/article/pii/S0960982218314179

(the genome of the kea has still not yet been sequenced..)

Wirthlin et al. (2018) comparison with 30 other bird species (not including corvids) revealed parrot-specific changes in gene expression that are associated with cognitive abilities in humans.

https://link.springer.com/article/10.1007/s10071-022-01733-2

From the vague notions I have of embryo selection by reading posts here, I expect that you could improve the parrot by an important by parrot standards amount, but not get to genius parrot without either: long timeframes, new techniques, major expense.

Initially, the genetic variations you would be selecting would mostly have independent effects, so you would not be slowed down by compromises with side effects. But I expect this linear regime to break down at some point. I have three scenarios in mind:

1. The linear regime: each genomic variation contributes independently to metrics you care about, and in the same way in each generation of parrots.
2. The linearized regime: like (1), but the way the variations contribute changes every few generations as you select your parrots.
3. The nonlinear regime: at some point you can't quickly pareto-improve the parrots with embryo selection based on looking at correlations between variations and metrics. You have exhausted your "linear modifications budget".

In this framing, I consider (2) more probable, because I think evolution needs at least (2) to work, and (1) would make evolution too fast. But I'm not confident.

What happens to your plan in each scenario:

1. You can use the genomic studies done on existing parrots to select embryos all the way up to your genius parrot race at a steady pace.
2. You need to create a very large population of generation-locked embryo-selected parrots every once in a while and redo the genomic studies, so it's more expensive than (1) without changing time frames.
3. You will get stuck at somewhat more intelligent parrots, and then need major scientific breakthroughs.

No, on two levels:

1. Nobody is trying to breed intelligence in any creature.  It's just not a thing.
2. There's no reason to believe that your "advantages" matter at all.  Any of them can be overcome with breeding/engineering, probably more easily than getting to human-level intelligence.  The only thing that matters in breeding is how far the target is and generation/selection latency (how fast can selected individuals reproduce).

If intelligence is your goal, and breeding is your main tool, you should probably focus on humans.