I'm trying Uniform Server 15.0.2 on Windows 11 to support a local Wordpress. Today's package provides phpMyAdmin 5.2.1. I updated to 5.2.3 basically following the above.
The 5.2.3 zip file from https://www.phpmyadmin.net/ had some extra stuff that I didn't use.
Renamed .../UniServerZ/home/us_opt1 to su_opt1 - 5.2.1, just in case...
Copied all the files from folder (download), phpMyAdmin-5.2.3-english to .../UniServerZ/home/us_opt1. This overwrote most everything, but not touching config.inc.php and us_opt.ini.
It also left the old RELEASE-DATE-5.2.1 while adding RELEASE-DATE-5.2.3 read-me files.
Copied most of the directories (js to vendor) to us_opt1, replacing the previous folders (and contents).
I did not copy the new folders, doc and examples, since they did not appear in the original installation.
Restarting the UniServer console, Apache and MariaDB, I now have phpMyAdmin at 5.2.3 with prior data intact, and no nag about not running the latest version.