refactor!: HTTP and Gateway Apps

[VincentRPS]

Summary

This PR aims to replace Client and Bot with more useful and separated classes. Simply, the HTTP and Gateway bots, which are self-explanatory. HTTP bots will only support fetching, have no cache, and will hopefully allow for Pycord to support slash commands over HTTP. Gateway bots are essentially the thing everyone is already used to.

Information

• This PR fixes an issue.
• This PR adds something new (e.g. new method or parameters).
• This PR is a breaking change (e.g. methods or parameters removed/renamed).
• This PR is not a code change (e.g. documentation, README, typehinting,
  examples, ...).

Checklist

• I have searched the open pull requests for duplicates.
• If code changes were made then they have been tested.
  • I have updated the documentation to reflect the changes.
• If type: ignore comments were used, a comment is also left explaining why.
• I have updated the changelog to include these changes.

[pycord-app]

Thanks for opening this pull request!
Please make sure you have read the Contributing Guidelines and Code of Conduct.

This pull request can be checked-out with:

git fetch origin pull/238/head:pr-238
git checkout pr-238

This pull request can be installed with:

pip install git+https://github.com/Pycord-Development/pycord-next@refs/pull/238/head