feat: revamp search

[SychO9]

Closes #3884

Changes proposed in this pull request: Part of the roadmap, each commit has a separate PR. Changes are made one at a time for easier review/readability.

feel free to review within the related PR even if it's marked as merged.

Necessity

• [x] Has the problem that is being solved here been clearly explained?
• [x] If applicable, have various options for solving this problem been considered?
• [x] For core PRs, does this need to be in core, or could it be in an extension?
• [x] Are we willing to maintain this for years / potentially forever?

Confirmed

• [ ] Frontend changes: tested on a local Flarum installation.
• [ ] Backend changes: tests are green (run composer test).
• [ ] Core developer confirmed locally this works as intended.
• [ ] Tests have been added, or are not appropriate here.

Required changes:

• [x] Related documentation PR: https://github.com/flarum/docs/pull/467

[SychO9]

Feel free to leave separate reviews in each PR for easier back n fourth if necessary.

[SychO9]

Also, proof of concept search driver here: https://github.com/flarum/framework/pull/3902#issue-1949872262

[imorland]

Just need to resolve the conflict, then good to marge. Are you able to tackle that @SychO9 ?