* Always update the `_searchModesByBrowser` map when entering/exiting search
mode, not only for non-selected browsers, so that search mode can be saved and
restored properly per tab.
* Rename `setSearchMode` to `_updateSearchModeUI` and make it only update the UI.
* Add a new `setSearchMode` method that takes a browser and updates the map.
* Add `getSearchMode` so that SessionStore can get the search mode for a given
browser.
* Add a `searchMode` getter and setter for convenience. They call
`getSearchMode` and `setSearchMode` with the selected browser.
Differential Revision: https://phabricator.services.mozilla.com/D91910
a3eec99d1b
