Just a quick update:
Since the release of PHP8, we have had several WordPress updates and the most recent versions of WordPress appear to run well on PHP8.
However, the remaining problem remains the WordPress plugins and custom themes, which probably affects almost all active WordPress sites. Many plugins have still not yet been updated to make them PHP8 compatible. Indeed, some of the older plugins may never be updated, in which case you are going to need to find newer alternatives for the functions those old plugins add to your site.
That leaves us with this as the current status: You can try updating your site to PHP8 and see if it breaks anything. If you are on a site with WHM/cPanel, this can be done quite easily using the MultiPHP utility. If PHP8 breaks your site, you can simply roll back to PHP 7.4.
Alternatively, you can try disabling all your current plugins and then re-enabling them one by one to identify which ones are causing the problem. If you can identify one or more non-PHP8 compatible plugins, this is probably a good time to do some housecleaning — ask yourself if you really even need the feature(s) that plugin offers. If you really want to keep those features, start looking for a newer updated plugin that will do the same job.
If your site is still broken after disabling all plugins, you’re probably looking at a theme which needs to be upgraded — you can test this by seeing if your site can run with the latest WordPress default theme (Twenty Twenty One). If that works, it’s a pretty good indication that you need to update your theme, or if no updates are available you need to find a new theme.