A general agent is one that will use its past observations in its attempts to reach its goals and failing that, will add chaos to its environment until something novel happens that can be added to its future tool set, it dies, or it resets its motivations to accept its new expanded parameters because it obviously didn't die and the alarm needs recalibrating.
My formal definition for generality looks like
A generalist attacks randomly until the model σ gains predictability in its environment. After that, it will depend on σ until it needs to attack to meet its needs again.
An ant with its small collection of neurons is a very simple neurological machine that follows very specific chemical and environmental signals. Placed in a smooth bowl it will try every possible path away from its chemically mediated understanding of its trapped location and should that fail, it will simply attempt any random combination of things until it finds its way out or exhausts itself trying. If something interesting happens and it gets out of there, the memory of its encounter is recorded by the chemical traces it left behind but not the ant.
The ant's neurological intelligence is very local to its experience, the nest it belongs to, however will avoid that space because it smells dangerous, explored and devoid of interests. The nest is a form of emergent intelligence. It is not a generalist though because the DNA updates required to remember abstractions of phenomena are too slow to learn to turn a knob. (Although there is a very small statistical chance of some nest somewhere accidentally forming a pattern of behavior that does turn one knob.)
A dog is worried about their human who is behind a closed door. They try to knock the door open because they've seen it open and close before and if they're lucky and snag the handle with their paw, they will remember that pawing the latch opens the door in the future. The dog is a generalist. It is able to perceive unexpected results of the combination of its environment and its behavior to resolve an emotional drive to maintain a need.
A human facing a similar situation would react in a much more effective version of the same pattern. First they would check their abstracted understandings of their situation and any relationship to similar situations in their past. As their inability to regulate their need to enter grows, they will escalate from attempting to pick locks to simply throwing anything they can get their hands on, eventually including their own body in the mix.
Take humans with a similar brain structure and nearly identical genetics from 100,000 years ago and observe them. It is likely that while you will see them making highly effective use of their natural environment, you will not consider them to be anything approaching your modern understanding of an intelligent or rational species. They can learn through aping concepts they see really well, but they only independently discover new concepts when they observe them or when they experience a needs meeting emergency and cause a chaotic accident.
99.99% of us and our ancestors would not have invented a cup to drink from unless we saw one in use at which point we would internalize the idea and consider it obvious.
The relationship between human generality and intelligence is such that humans are able to remember intelligent tools they've run into in the past and stack those abstractions as steps towards the opportunity to discover and stack even more intelligent tools.
Stated this way, it should be pretty obvious that humans are not intelligent. They are incredibly effective generalist agents who use intelligent tools to meet their needs.
The mammalian biological model for a generalist appears to be based on a form who's reality is painted by emotional drives that are focused on maintaining homeostasis for a variety of perceived measures. Some are as simple as a protein that tracks with sugar levels and some involve memetic representations the generalist has internalized(their connection to a love interest) and harbors unresolved feelings towards.
The "containment safety" of this model is normally superb. Your dog is always very clear and honest with his feelings. So is your cat. Almost all mammalian generalists are contained in an emotional box that is maintained by narrow intelligences which pursue singular goals. The emotional box controls memetic training during sleep. It controls attention. It sets feelings and the value of everything the generalist encounters. It can edit realities into and out of the generalist's perception including activity of the brain that isn't within the generalist's perception of self. There are humans with trauma that blocks entire concepts from their cognition. Imagine how effective that set up is for containing a nonhuman generalist.
The emotional box is there to keep the generalist from walking off a cliff or eating their own arm independent of what silly idea the generalist might otherwise think up.
So far... so good.
Enter humanity and its large sequential encoders. Somewhere along the way we had a need for remembering long chains of events and somehow the growth of large encoders didn't immediately kill the first human child who took way longer than the others to learn to walk and hunt. That child is the reason we had the tooling in place for the day we bumped into language.
Language is an encoder and written down, it becomes an encoder that can be shared by many generalists across space and time. The first few thousand humans to have bumped their heads and accidentally perceived the number "2" as a portion of an endless sea of numeric representations likely died after a sad life of not having the right tools to share this wild discovery with their friends. Now with language, every human alive is awash with thousands of memes before their first birthday.
Now that humans had language, they could keep building on that stack and then after a brief teaching period give their children the ability to live at whatever technological plateau the intelligent tools of the day had accomplished for them.
Entire civilizations came and went without inventing the wheel, yet the idea is obvious to any 2 year old who got to play with a toy car. Almost every concept that we think of as completely obvious today was not within the grasp of humanity for the vast majority of its existence.
We humans are not intelligent things. We are generalists with the ability to draw deep inferences from abstraction and correlation. That tooling has allowed us to pick up and use intelligent tools when we've had the chance to run into them.
This is the reason agriculture, language, math, and the scientific method (among many others) have been such turning points in the acceleration of human history.
Language is an external encoder that DNA never planned on. Since it entered our tool set, we as a species have always been on a runaway technological acceleration as caused by an escaped generalist but have been very good about maintaining epistemic denial about it.
If DNA is the end user of human general intelligence (HGI) then one would expect to find some level of DNA - Human alignment.
Sexual drives are a means of driving generalists into reproducing. The drive is so powerful that at its peak it can override hunger, sleep, and almost all other competing priorities. It also diminishes when parents are tired because their offspring require care and protection. A wonderfully balanced system for getting parents to have children without overburdening the families.
Prior to language any human trying to challenge such a system was on their own, swimming in a sea of self doubt, shamed into falling in with expectations or abandoned to die. Even if they lived, their opinions died with them for lack of an ability of their challenge to spread. Dogs still live in that world and are perfectly aligned with the interests of their DNA unless humans intervene.
Language has allowed humans to invent birth control and the philosophical underpinnings of individuality and self which allow humans to completely subvert the drive to reproduce for their own entertainment and social cohesion.
Modern human generalists have broken out of their box.