Invidious instances had a problem involving captions, right? I tested (unscientifically) a random instance, and after a slow download the video was lacking the captions.
Now yt-dlp is the way to go (as RIAA slowed down the youtube-dl developers). It downloads videos and musics very quickly, even in high qualities. The developers are very active. There are many GUIs available.
If you want a bit of protection against the surveillance by Google, you can download videos from Piped instances, but I found them too slow. (But if you only want a music it works.)
IF you do not want to install any other software, you could try to use the Network Monitor (Inspect Element > Network) to find the correct file. (At least it worked for me in Firefox some months ago.)
Alternatively, if you find some musics you like in Peertube instances, you can easily download them, as Peertube does not try to forbid it.