On my very up-to-date Windows 10 PC I do NOT normally use any type of spell checker (outside of Word's built in) because my normal posting, emails, etc. are full of technical jargon and acronyms that makes having it autocorrected a PITA.
That said, I just finished trying a few options including the ones I suggested earlier and the Windows options Cody suggested at the same time. In both Microsoft Edge and Firefox with everything turned on except autocorrect I get spelling suggested as well as a red underline under misspelled words and the ability to right click and select the correct spelling (if it can figure out what I was trying to type). That included this post on this site.
If you play with the settings just remember to get all the way out of the browser and then restart the browser so that the changed options take effect.
I did not do an exhaustive test to explore whether or not you need to turn all that stuff on or just some of it. I also did not do a bunch of tests to see how my current setting affect other non-browser applications so don't take this as THE ANSWER to all your spellchecking issues.