Does Cloudflare Pro Plan allow to increase timeout limit in order to avoid 524 errors?

Suggestions regarding 524 error:

That’s correct, but if you have selected Cache Level: Standard (without Page Rule) for your domain, the CSS and JS files are cached (HIT) too (at least for me - or it’s due to my origin cache setup).

Due to my curiosity, may I ask which WordPress request or a plugin needs more time than that to execute something?
You stated “publiush/edit posts” - that should be in 100 seconds.
Have you tried troubleshooting / debug the MySQL and PHP process(es) at your origin host / server?
WP Cron or?

I afraid no, Cloudflare only offers that kind of customisation on Enterprise plans.