Firefox

I use freetube, https://github.com/FreeTubeApp/FreeTube

I don't think it has a mobile version

It might not quite be what you want because it doesn't rely on YouTube's algorithm at all. You subscribe to channels and freetube will show you videos from those channels. Well I guess you can view trending videos and such but it isn't personalized.

One downside is I find it difficult to discover new channels because there is no algorithm recommending stuff. Watching a video and then looking at the 'up next' list is helpful though.

This may not be exactly what you're looking for but have you considered using Firefox containers, automatically logging in to a different Google account for each container? I'm fairly sure this would work on mobile (probably only Android though), and is almost certainly more convenient and polished than a separate YouTube client.

I'm aware of FreeTube and PlasmaTube, which IIRC both require an Invidious instance. There was something called SMTube in the past, not sure if it still exists.

Nothing I'm aware of has both desktop and mobile version, but if anything there are more options for mobile YouTube clients; try NewPipe or Clipious.

Edit: SMTube does still exist. It does not require Invidious, but it does use tonvid.com.

The only Desktop native YouTube client I know is PlasmaTube (I think it's made for Plasma Mobile), which uses Invidious backends, might not be what you're looking for.

Friendly reminder that multiple accounts will not be sufficient to compartmentalize your youtube activity, since google will still see your IP address and client/browser fingerprint. Using different clients through different VPN (or proxy) sessions can help there.

PlasmaTube

The Unix way: sfeed + mpv + yt-dlp