refactor: replace Fomantic search module with first-party code (#37443)

- Replace fomantic `search` code with minimal first-party code
- Added a small fix to vertically align search box and search button
- Manually tested all search forms.
- Add `errorName` helper, similar to `errorMessage`.

Signed-off-by: silverwind <me@silverwind.io>
Co-authored-by: Claude (Opus 4.7) <noreply@anthropic.com>

web_src/fomantic/theme.config.less

@@ -44,7 +44,6 @@
 @progress   : 'default';
 @slider     : 'default';
 @rating     : 'default';
-@search     : 'default';
 @shape      : 'default';
 @sidebar    : 'default';
 @sticky     : 'default';