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Very nice, not what I expected and worth a read!
I had no idea what this was talking about and followed links to a blog post that explained the first one ("Bigfoot"): https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html

This blog post made the "cryptids" make a lot more sense to me, so I thought I'd share that post here in case others were also wondering "what the **"

these remind me of rule 110 in GoL https://en.wikipedia.org/wiki/Rule_110

are they related?

Weeell, sure, in the obvious sense that 110 is Turing complete. So you can encode any of these cryptids as a 110 initial pattern.
You can encode any Turing machine as initial state for rule 110, but as far as I know it isn't useful for studying Busy Beavers.
If we can't predict/model these Turing machines' behavior because of unsolved math problems, what's stopping us from actually creating and running them to see what would happen (and maybe getting closer to solving those math problems in the process)? Is it just a matter of scale and resources?

My knowledge here is very limited, so this isn't a "why has no one tried this one weird trick"-type question. I assume there is in fact a good reason that I don't yet understand :P

That only provides a proof if the machine halts in a number of steps that you can compute. Otherwise, it is unable to determine whether the machine halts later or doesn't halt at all, which is the current situation.
Getting some Disco Elysium vibes here.