I'm sure you've thought of this, but: lots of people have some amount of 'free' (or really: zero incremental cost to users) access to some coding chat tool through a subscription or free allowance like Google's.
If you wanted to let those programs access your custom tools (browser!) and docs about the environment, a low-fuss way might be to drop a skills/ dir of info and executables that call your tools into new installs' homedirs, and/or a default AGENTS.md with the basic info and links to more.
And this seems like more fuss, but if you wanted to be able to expose to the Web whatever coding tool people 'bring', similar to how you expose your built-in chat, there's apparently an "agent control protocol" used as a sort of cross-vendor SDK by projects like https://willmcgugan.github.io/toad-released/ that try to put a nice interface on top of everything. Not saying this'd be easy at all, but you could imagine the choice between a few coding tools and auth info for them as profile-level settings pushed to new VMs. Or maybe no special settings, and bringing your own tools is just a special case of bringing your own image or setup script.
But, as y'all note, it's a VM. You can install whatever and use it through the terminal (or VSCode remoting or something else). "It's a computer" is quite a good open standard to build on.
Is the chat descended from Sketch?