They might decide not to counter-notice, because there's a big trap in the DMCA counter-notice: as far as I know, for a DMCA counter-notice to be valid, the one doing the counter-notice must agree to be bound to the jurisdiction of an USA court. If the youtube-dl author is not from the USA (I think he's from the EU), that would expose him to legal risk.
(As a non-USA person, to me this is the most evil part of the DMCA take-down system: even a defective DMCA notice leads to a dilemma, either you keep the content offline, or you risk being sued in a foreign jurisdiction you have no control over. This is also why I believe one should always prefer to host in one's own country, so that any dispute can be resolved by the local courts.)
The biggest thing a counter-notice could do (if it's even possible) is reveal one's identity and only if Microsoft/Github tries to verify it, which would be bad, because it could be used for harassment. But the author is obviously Russian, not sure if he lives in Russia, but if he does, they definitely won't be able to get him in Russia, only harass him.
[1] https://www.eff.org/deeplinks/2020/11/github-youtube-dl-take...
The recourse is filing a declaratory judgement to establish the legality of the code.
Which is expensive relative to the resources of some individuals doing this as a hobby, so some kind of legal defense fund may be in order.
Of course, the other option is to put enough pressure on Github/Microsoft to get them to be the ones to defend it, since it's not that expensive relative to the resources of a trillion dollar corporation, and they could quite plausibly have more to gain in positive PR with developers (or in avoiding continued negative PR) than they pay to the lawyers they probably already have on staff.
We shouldn't forgive companies who do the wrong thing on issues like this, because the cost of people not forgiving them is a major incentive for them not to do the wrong thing.