How can I create a background process on the site?

Question

PHP

It is required that by pressing a button on the site, after a while the value in the database changes. We want this to happen even if the user has navigated to another page or closed the site.

Answer 1

It's not clear from the description how it should work.
As one of the options:
1)

at the click of a button on the website

write data to a separate table.
2) set the cron task to the right one

over time

, for example, every hour, minute, or the like.
3)

even if the user has moved to another page or closed the site.

cron will pull the script you need. In it, you get the data that users clicked and process it.