They only spend money on some minor infrastructure to have JIRA and the mailing lists and build servers running; plus administrative / legal personnel.
All the new "Apache" software is written by volunteers, the mirror system is provided free by 3rd parties, code hosting is almost all on GitHub.
So, what would they need the extra money for? Another JIRA instance?
By comparison the FreeBSD foundation does hand out grants to fix parts of their OS which they deem relevant and in need. Would be nice to see something similar in other foundations.
So, the answer is that nothing exist.
Out of the given options a few also don't qualify (like I mentioned, Apache for sure, opensource.org most likely) because they don't spend money on software development at all.
Why isn't there a public open-source fund [...]
I know it doesn't exist. The non-existence thereof was what prompted that question. I have no idea what point you're attempting to make.
I do apologise for replying to you. If only HN would have a feature to block me from replying to you in the future.