I have used Flywheel to host my website, however now all updates show a fatal error. When I update the plugins, it comes back with Update failed, this is the error prompt message: There has been a critical error on this website. Please check your site admin email inbox for instructions.Learn more about troubleshooting WordPress. I also try to upgrade the wordpress version, but it also failed, I am able to start the process and see the files get downloaded into the upgrade directory, the .maintenance file was created, the lock on the database is created, finally it hangs.
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You can find out the reason via error log, this is the best way to look into the error.
Another way is to enable debugging in your website. Here is the steps for you to enable it: https://wordpress.org/support/article/debugging-in-wordpress/ .
Two solutions requires you to be able to see what the cause is in the logfile. Often it is a plugin. You can delete the directory of the guilty plugin via FTP. After that, I think you should be able to access your website again.