[Feature Request]: Override default video player settings / Retain player settings within session

### Guidelines

- [X] I have searched the [issue tracker](https://github.com/FreeTubeApp/FreeTube/issues) for a feature request that matches the one I want to file, without success.
- [X] I have searched the [documentation](https://docs.freetubeapp.io/) for information that matches the description of the feature request I want to file, without success.

### Problem Description

When https://github.com/FreeTubeApp/FreeTube/issues/2263 was opened up. I noticed how many issues were actually opened for the same request. So here we are making a big summary.

Why do we want this? Let say in the settings i have set my default video quality to 1080p. My internet provider is giving me a hard time today so while im watching a video i switch from 1080p to 360p in the video player. The next video should also run in 360p because i just have overwriting the default quality because my provider giving me a hard time.

I could write usecases for the rest but i assume u get my point. U change it in the player for a reason.

### Proposed Solution

Player buttons from the left to right, that already do this.

- [ ] Volume
- [x] Autoplay ¤
- [ ] Audio Tracks (i.e., stable volume)
- [ ] Captions
- [x] Playback speed ¤
- [ ] Resolution
- [x] PIP ¤
- [x] Theatre mode ¤
- [x] Fullwindow ¤
- [x] Fullscreen ¤
- [ ] Dash/Legacy/Audio Formats

¤Persists through contiguous viewing session (i.e., until leaving the Watch page)

### Alternatives Considered

I do understand that some people like it that the default settings overwrite the player settings when a next video is being played. We maybe could have 2 modes?

1. Player settings is always overwritten by default settings when another video is being player.
2. Player settings dont get overwritten and stay like u set them to be for that session.

### Issue Labels

ease of use improvement

### Additional Information

I understand that this will be a difficult and long discussion. The point of this issue is to centralize the discussion to this issue instead of 8 other issues.

Allot of discussion has already taken place [here](https://github.com/FreeTubeApp/FreeTube/pull/1281).

Most important bit of discussion is [the settings scope manifesto](https://github.com/FreeTubeApp/FreeTube/pull/1281#issuecomment-912846345) provided by @jasonhenriquez