How does tinydns deal with it? Does it need patches? Are they available? I don't see it mentioned.
I don't know of any latest-version DNS software that breaks in this case. AFAIK this is exclusively a middleware problem, as is quite often the case.
It does not exhibit any of the faulty behaviours that are common to bad EDNS0 implementations. It does not blindly echo various parts of the query back in the response, for example. Indeed, the ISC test actually complains that tinydns does not blindly echo an OPT record back. (-:
But you cannot speak DNS/UDP to it with datagrams over 0.5KiB. Patches are needed to make it do anything but wholly ignore EDNS (of any version) and treat it as though it were the unextended protocol. But that is not what this flag day is about.
Indeed, given that tinydns does not send DNS/UDP responses greater than 0.5KiB, it does not trigger any EDNS0 problems in the network infrastructure that a server is using, either.
Ironically, one of the people who tried to rewrite djbdns to have EDNS0 support discovered exactly the problem that this flag day is about: The bad content DNS servers for outlook.com in 2017-2018 gave bad responses to clients that attempted to speak EDNS0.
Needless to say, after tons of time getting into the weeds with EDNS, and STILL not understanding why certain clients weren't working, that was a fun one to solve.
The home page mentions that EDNS queries will be honored even for non-DNSSEC queries.