Well, this is where the chaff separates from the wheat. There's no small amount of crappy code out there which will WSOD after this. Or actually print the exception because they couldn't even bother to switch display errors on... Of course, no even remotely sane codebase will be affected, but... Make no mistake, this is a good change but it will cause some teeth gnashing.
Undefined variables will now be warnings (and one might expect PHP 9 to reclassify them as exceptions).
But I will not be surprised to see some people say things like “PHP 8 broke my code”. Of course, what those people might not realize is that PHP 8 did not break their code, the code was always broken, and PHP 8 is now going to surface the brokenness of that code.
But even with code that people refuse to fix, this sort of change will make the brokenness of that code more apparent to others, and so the number of people that use that broken code will cease to grow. If not entirely, then at least reduce in pace of growth.
That is good for the ecosystem of computing. As a proponent of correctness in computing, this makes me happy :)
We all write bugs, but everything our tools and languages of choice can do to help us reduce the number of bugs and the severity (impact on security) of our bugs, the better.
Personally, I think a lot of these design decisions which some people abhor is why PHP became popular in the first place. In that perspective, turning it into yet another "big bureaucratic language" is very much against the spirit of its existence.
To stop the warnings, configuration would need to be changed in PHP config, or those warnings be silenced by the developer.
Any decent webapp has had this issues resolved a long time ago.
I would suggest that websites that will be effected probably will not migrate to PHP 8 that quickly.
But there are a million questions on the internet about this 'error'. And the answer is almost always: turn the errors off.
And I believe this is the biggest problem with PHP. A lot of inexperienced users with questions that get very bad answers.
For a development and staging website you do want notices and warnings displayed. For a production website possibly only when testing something.
Just SSH in and tail the log. Dealing with unexpected output from errors clobbering your headers isn't worth the trouble.
You can also try something like FirePHP [0] if you need the errors in the context of the current page.