I pay $20 for ChatGPT, and I can use it on OpenCode without paying extra. I haven't tested Claude. Is it much more powerful?

Similar, depending on the situation at the time (compute, model quality etc.) one may be better than the other. Harnesses (like OpenCode) are regularly updated too which may result in different results even if using the same exact model.

I think that the proposal is great, but it's bad timing, I guess. Why not create the fund some other way? Why use the DHF?

Out of curiosity, how?