(I didn't have much time to write this so it is kind of off the cuff. It also only answers part of your question, but I think it's correct and hope it fills in some of the gaps for you.)
The leading labs publicly working on AGI seem to be OpenAI, DeepMind and Anthropic. Microsoft is heavily invested in OpenAI, while Google/Alphabet owns DeepMind and has some investment in Anthropic. There is also Google AI, which is confusingly separate from DeepMind.
Meta (Facebook) AI is also working on AGI, as are a number of lesser known startups/companies, academics and orgs.
I have heard there are at least one or two labs in China working on AGI, though I know less about the landscape there. There may be other companies/countries privately working on AGI as well.
I mentioned this in the context of AGI, but if you broaden that to include companies working on narrower ML systems, well there are tons of companies doing that.
Which actors (countries, companies, individuals) are currently taking part in the AI race? Who may be, for any reason, the most problematic? I tried to find posts about it, but ended up not being very successful.
I'm pretty new to the field and would like to understand the full picture better.