Disable custom ESLint rules for //ui

Most of the custom rules were unnecessary. //ui/file_manager was given a
1-month exception. The rules were hoisted into src/.eslintrc.js for that
time. The eqeqeq rule, which is in the process of being applied to the
whole codebase, is migrated to toplevel .eslintrc.js.

This CL was verified with
`git cl presubmit --files "ui*.js;ui*.ts"`.

I confirmed that the eqeqeq rule correctly applies to //ui by manually
modifying a file to break the rule, and confirming that an error
triggers in presubmit.

Change-Id: Ib913f724898f4cd3befcfec9577b8e328249560b
Bug: 369766161, 368085620
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/5894200
Reviewed-by: Demetrios Papadopoulos <dpapad@chromium.org>
Reviewed-by: Luciano Pacheco <lucmult@chromium.org>
Commit-Queue: Erik Chen <erikchen@chromium.org>
Cr-Commit-Position: refs/heads/main@{#1361670}