It is problem which haunted me for few days with bunch of diagnostics, but then I found solution (it is Windows only, but it is portable application) – Laragon.
After migrating site to it (copy local files and import SQL file using phpmysql from Laragon, change password, username and db name in wp_config.php) you will see that it will work just fine.
Few notes: in Settings of Laragon change Hostname template from {hostname}.app to {hostname}.local so it don’t need changes for domain in SQL table wp_options
There you can setup custom env and even test site with PHP8.0 and 8.1. Plus it is waay faster then Local which is slow, even for small changes as app is loading files from multiple locations (at least on Windows), while Laragon is fast and have better SSL support.
