Update: So if you run the server locally and select maps, you're presented with this screen, saying you need a key from openmaptiles.com: https://i.imgur.com/NTb5zIL.jpg.

If you select "commercial product or company web", you're asked to pay for it: https://i.imgur.com/TrAmju4.jpg

If you select any of the non-commercial ones, the newest map data you get is from 2017 (!).

I'm not against paying, but it's not free!

It's a little unclear to me. But from what I can gather, the basic software can download data from OSM, but if you want hillshading or satellite, you have to get that separately, and it's part of the $1,000 "production package" [1], which is actually $2,048 for businesses, plus $1,024/year for updates.

[1] https://openmaptiles.com/production-package/

Forgot to answer about styling. Yes, looks like custom styles with the production package (which has hillshading, which ends up making the maps look much nicer) is much better. For some reason their main demos don't show off their best map styles.

Only if you're below 500k raster tile downloads per month. The app I need this for is at 5.5m/mo, so it'd be a little more than $245/mo. Still better than Mapbox, though.

Mapbox's tiles are very good. I particularly like the hybrid terrain + road mode, which you can see here: https://homes.stltoday.com/search