[Feature Request] Piped support for YouTube

Nobody has claimed this yet.

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

Not that I am aware of.

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

I would like to be able to configure the bot to utilize my Piped instance when playing back Youtube videos.

Piped: https://github.com/TeamPiped/Piped
Their API: https://docs.piped.video/docs/api-documentation/

I host my own instance, it'd be neat to use it - or at least have the links be recognized.

### How would this feature be used?

When using `!play `, the bot checks if the URL matches the configured Piped instance, fetches the apropriate Youtube URL, and continues from there on as normal.

### Additional Info

Nothing I can think of, really.

### 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: 

Start at the !play URL handling and review the Piped API documentation linked in the issue. Done means a configured Piped instance can be recognized, the appropriate YouTube URL is fetched, and playback continues through the existing flow.

Written by the indexing model from the issue text.