I bought a small steam cleaner and it works better than anything I've ever used. No scrubbing, just steam and wipe up the dirty water. I have tile kitchen counters (1983 issue) and what a difference it has made! My bathrooms have new tile with epoxy grout and it never needs scrubbing because nothing sticks to it, or grows on it, or stains it. I read to not use a steam cleaner on epoxy, but on another thread someone says she uses steam on her epoxy with no issues. YMMMV, This is the model I have and it works great. Lots of other choices, too.

Steamfast steamer

Once you get it clean, look into sealing it so the dirt doesn't settle in again.

Grout renew.

I think I've been "meaning" to get to the grout on my kitchen floor for a few years now and each time I research it, I get confused by all the different recommenations.

I just googled again, and came up with this summary articleHere's the link

Pretty good article from Jan 24. The Spruce.

I still haven't acted though.

Equal parts Hydrogen Peroxide and baking soda.