Sourcerer should work fine on PHP 8.

Can you give me (super) admin and (s)ftp access so I can take a look?
And tell me on what url I can see/reproduce the issue.
You can use the 'Confidential information' button in the forum editor to hide sensitive information.

I have checked a few pages on the frontend, but I don't see the codes anywhere.

I cannot log into the administrator either, as the captcha image is not working.

You shouldn't be switching PHP versions and updating/upgrading stuff on a live site, to begin with.
First test on a test copy of your site.

So once you have your test copy up and running, and can reproduce the issue, then you can give me access to that.

I could not log in via ftp. Credentials don't seem to work.

I tried to open the edit page for the Yoo template style, which resulted in a broken page. So stuff is not ok there either.
Then I switched on Error Reporting in your Global Configuration.
That resulted in a bunch of fatal errors, and I can't even switch that option back off.

It looks like you have some serious issues on your site.

You can undo the error reporting by manually editing the configuration.php.

So first step after that for you would be to fix all the issues you have on your setup.
Chances are that whatever those issues are, is also preventing the Sourcerer plugin (and maybe others too) from running.

You'll have to fix the issues I mentioned earlier before it makes sense for me to look into this any further:Check the template style...

Also, see if you can reproduce the issue with the Joomla core template.
I think this is all down to the template... not Sourcerer.