Do platforms like Grayjay or YouTube frontends like Invidious really offer that much more privacy than just using the YouTube website, logged out, with a VPN on a private tab to clear cookies? I’m thinking maybe for subscribing to certain channels, but what other benefits are there other than just making it slightly more inconvenient?
For convenience sake, no not really. Invidious from my experience is a terrible right now for watching YouTube because they are often slow and get blocked by YouTube. There are very few instances right now. If Javascript tracking is a concern to you though, Invidious and other clients can help with it.
Clients like Grayjay, Invidious, Freetube, Piped, etc, are really just to save playlists and subscribe to channels (unless of course, you don’t use a VPN, in that case, it gets rid of IP based tracking).
Use RSS and you will be doing just fine. PrivacyGuides has a great page for clients: News Aggregators - Privacy Guides.
If you do that, you’ll encounter the same problem on Youtube then on all the other apps you mentioned. “Sign in to confirm you’re not a bot.” You will be forced to sign in to Youtube.