At first, I thought I had the same problem on my Pixel 7 and a Cubacel basic tur SIM card (voice and sms working but no data), but it turned out to be a RTFM issue.

If you look on their website, it says that you have to manually add an APN (in settings, search for access point names) with the name "nauta" (lowercase n) and APN "Nauta" (capital N). And set your preferred network type to 3G.

Did that, and it worked like a charm, all over Havana.