This may well be an add-on issue, but the same add-on on two other Kodi devices (Vero 4K+ and Amazon Fire TV Stick 4K) isn’t exhibiting the problem, so I thought it was worth checking that there isn’t something happening on the OSMC side.
I’ve gone through the process of generating some YouTube API keys. On the Vero 4K+ I’ve installed them (via the API web interface) and they work perfectly there. I’ve also copied and pasted the keys to another device in the past (Fire Stick) doing a c&p between the API web pages, and that also works perfectly.
But copying the same keys into the Pi’s API web page and then signing in gives me an error: “Client Id is incorrect. Settings - API - APi Id”. I’ve checked the API Id several times, and it’s definitely the same as the one on the Vero 4K+.