WPCS-modernize the relocated inc/ files and drop their PHPCS exclusions

> *This issue was generated by AI.*

Follow-up to #1061 (split `wp-cache.php` into `inc/` files, PR #1065 / ADR-0001).

## Background

The split relocated legacy procedural clusters **verbatim** (pure move, no behaviour change). Each relocated file carries pre-existing WPCS debt — loose comparisons (`==`/`!=`), non-strict `in_array`/`array_search`, missing escaping, legacy spacing, etc. To keep the move behaviour-preserving and the PR lint-clean, those files are **excluded from PHPCS** in `.phpcs.xml.dist`:

- `inc/plugins-cookies.php`
- `inc/cache-files.php`
- `inc/htaccess.php`
- `inc/settings-forms.php`
- `inc/preload.php`
- `inc/lifecycle.php`
- `inc/admin-notices.php`
- `inc/admin-ui.php`

(`inc/boost.php` and newly authored files are **not** excluded and stay fully linted.)

## Goal

Modernize each excluded file to satisfy the repo's `.phpcs.xml.dist` standard, then remove its `exclude-pattern` so it is linted again.

## Constraints

- **Behaviour-preserving.** Several flagged rules are not cosmetic — `==`→`===`, non-strict `in_array`/`array_search`, and `@`-silencing changes can alter behaviour. Verify each change against the test net (`composer test-php`, `make test-integration`, `composer test-e2e`) rather than blanket-applying `phpcbf`.
- Do it **one file per PR/commit** so each is reviewable and revertable, and so the changed-lines linter stays manageable.
- Note: full-file `phpcs` on these big procedural files aborts on a pre-existing PHPCompatibility `Internal.Exception`; run it with `php -d error_reporting='E_ALL & ~E_DEPRECATED & ~E_USER_DEPRECATED'` to get the sniff list (see how #1061 surfaced them).

## Out of scope

Global-state reduction / class extraction (that's the deeper follow-up, e.g. turning `inc/preload.php` into the #1047 item-5 preload state machine). This issue is WPCS cleanup only.

Start with the eight excluded paths in .phpcs.xml.dist and inspect one relocated inc/ file at a time. Run PHPCS with the specified PHP error_reporting setting, then verify behavior with composer test-php, make test-integration, and composer test-e2e. Done means the selected file satisfies the repository standard and its exclude-pattern is removed without behavior changes.

Written by the indexing model from the issue text.