[Feature Request] yt-dlp for Youtube

Nobody has claimed this yet.

### Is your feature request related to a problem? Please describe.

*Since this repository seems to be dead, i will direct this question/suggestion for the numerous forks that are active but doesn't have the Issues tab enabled, mainly @Eddie0343, @antronic, @PoH98 and others*

I wonder if switching to [yt-dlp](https://github.com/yt-dlp/yt-dlp) (with help of ffmpeg too, if necessary) to fetch Youtube links instead of the current methods (lavaplayer, YT API) would solve the multitude of issues that appeared when users try to play youtube songs with the bot.

### What is your ideal solution to the problem?

n/a

### How would this feature be used?

n/a

### Additional Info

_No response_

### Checklist

- [x] I have checked [the documentation](https://jmusicbot.com/) to make sure this feature doesn't already exist
- [x] I have searched for [similar feature requests](https://github.com/jagrosh/MusicBot/labels/enhancement)
- [x] I have confirmed that my requests is **not** on the [list of things that will not be added](https://jmusicbot.com/things-that-wont-be-added)
- [x] I am running the latest version of the bot: 

Review the bot's current YouTube playback paths using lavaplayer and the YouTube API, then compare them with the proposed yt-dlp and ffmpeg approach. Define the supported playback behavior and failure cases before implementation; the issue names no files or tests to begin with.

Written by the indexing model from the issue text.