chore: bump typescript-eslint to v8

[JoshuaKGoldberg]

Changes

Similar to #7425, this:

1. Updates typescript-eslint dependencies to the v8 beta (https://typescript-eslint.io/blog/announcing-typescript-eslint-v8-beta)
2. Fixes straightforward new complaints
   • These were mostly from @typescript-eslint/no-unused-vars now flatting unnecessary catch variables
   • Some rule renames also were needed, mostly from https://typescript-eslint.io/blog/announcing-typescript-eslint-v8#replacement-of-ban-types
3. Disables not-so-straightforward rules in the ESLint config
4. ...and that's it - unlike chore: use typescript-eslint@v8's projectService for typed linting #11315, doesn't enable the new project service (because it's not quite ready for this complex a repo!)

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[bluwy]

Looks great! Maybe we can look into properly setting up projectService in the future.

[Princesseuh]

what a dream it is to be able to remove these, thank you eslint team 🙏