To the original poster, locate your wp-config.php file in your wordpress root directory, open in a text editor like notepad and find the line that says DEBUG=false, change that to true. Refresh your webpage and you will get a read out of errors that it is encountering. A critical error could be anything, but it most likely comes from the 8.1 error in the way it connects to mysql. I posted a link to a fix for that with example code. Then after that you will probably get another error telling you that there are no tables present in the database, you will need to pass the flag mysql_native_password in MySQL. The latest versions of both PHP8.1 and MySQL8 made code change that seems to conflict with latest version WordPress. Again these are just simple one line modifications that is part of any server administration.
I have heard several times that the latest version of WP is not compatible with php8.1. I am running it without errors, although I will admit there was the one modification that had to be addressed. This was a change in reporting with mysql database, a single line of code fixed the problem. So its not even that PHP is compatible with wordpress, its simply the way it interacts with Mysql.
