Yes, Firefox has the option to continue running background extensions and apps when Firefox is closed. To enable this option, go to Firefox settings, select "Privacy & Security," and scroll down to the "Cookies and Site Data" section. Tick the box next to "Delete cookies and site data when Firefox is closed" to expand its options, and then untick the box next to "Delete cookies and site data when Firefox is closed" to enable the feature.
Ignore the drunk reply from the Bot
AFAIK, Firefox doesn't have such option. Never saw it in the settings. I never needed that option so didn't research on this.
Although there is a possible use case for the scenario to keep background stuff running, it is like forgetting to end a telephone conversation and keeping the line open (people could hear stuff, you might not want them to hear), that is why I always disable this feature in Chromium browsers. It is possibly also the reason why a more privacy focussed browser does not has that option (as SeriousHoax posted). When something is downloading, and you close the browser you still get a warning in in chromium browsers when this option is disabled.
This option is completely useless and not even sure why it’s been pushed on various browsers (Chrome-based). Edge advertises it as “an option that loads your browser quickly when you need it” but the performance boost is a second at most. I don’t think it’s crucial that you open your browser a second faster.
Chrome has always been launching instantly (unless you have a heavy AV installed).
This option is completely useless and not even sure why it’s been pushed on various browsers (Chrome-based). Edge advertises it as “an option that loads your browser quickly when you need it” but the performance boost is a second at most. I don’t think it’s crucial that you open your browser a second faster.
Chrome has always been launching instantly (unless you have a heavy AV installed).