...Irrelevant? That's the whole point. "Taking donation via a separate website (emphasis in original)" is explicitly dissallowed in the Play Store (and App Store on iOS)! There happens to be an exception carved out for federally-registered charities. But no, you don't get to just hold out a link to a tip jar.
Does this link count as a charity? No, per the structure of federal tax law. Also no, per the set of rules of the app store it's trying to be listed on. Should it count? Well, maybe I guess? Open source projects are like charities in some cases. We should all want to support them. But doing it like this, through a middle-man organization that isn't a charity, just plain smells like fraud to me. Who's doing the auditing that this is just supporting development and not profit centers? Is the IRS doing it? Not as far as I can see.
"Phone apps" is irrelevant, because again, Anki was not taking donations via their app but rather via a link to OpenCollective, a separate website.
So the remaining part of your question:
> Do LF and Rust solicit individual donations (at all, really)?
Yep, the Linux Foundation has a PayPal donate button (with a simple note to U.S. taxpayers that it's not deductible): https://www.linuxfoundation.org/about/donate