chore: migrate more tests to new test suite

[Garmelon]

This PR migrates most remaining tests to the new test suite. It also completes the migration of directories like tests/lean/run, meaning that PRs trying to add tests to those old directories will now fail.

[mathlib-lean-pr-testing]

Mathlib CI status (docs):

• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase fe1ad52f88a2b72913f9cb5f218146cb5a0c584f --onto 333ab1c6f0ce11f33551d6a736054cb72812cad9. You can force Mathlib CI using the force-mathlib-ci label. (2026-03-05 13:20:57)
• ❗ Batteries/Mathlib CI will not be attempted unless your PR branches off the nightly-with-mathlib branch. Try git rebase 6ebe573c197acc541f66e3006a6275727ef627c5 --onto 333ab1c6f0ce11f33551d6a736054cb72812cad9. You can force Mathlib CI using the force-mathlib-ci label. (2026-03-05 21:31:23)

[leanprover-bot]

Reference manual CI status:

• ❗ Reference manual CI will not be attempted unless your PR branches off the nightly-with-manual branch. Try git rebase fe1ad52f88a2b72913f9cb5f218146cb5a0c584f --onto cda84702e9b31165f1f83c657b532f36f34e0bd0. You can force reference manual CI using the force-manual-ci label. (2026-03-05 13:20:59)
• ❗ Reference manual CI will not be attempted unless your PR branches off the nightly-with-manual branch. Try git rebase 6ebe573c197acc541f66e3006a6275727ef627c5 --onto cda84702e9b31165f1f83c657b532f36f34e0bd0. You can force reference manual CI using the force-manual-ci label. (2026-03-05 21:31:25)