SMS - this requires a mobile connection and should be receivable so long as you have signal and roaming enabled. No mobile data or WiFi needed.
RSC - like more proprietary formats such as iMessage and WhatsApp etc. are sent using data. You either need a WiFi connection or mobile data.
You say you’ve activated mobile data but then say you haven’t purchased any data. Does that mean you’ve enabled it but can’t surf as you have no data roaming? If so, then that’ll be why RSC messages don’t work.
Assuming you’re connected to a mobile network (data NOT needed) then SMSs should be receivable free of charge.
The fact you say you receive SMSs when connected to WiFi means they’re not actually SMSs but RSCs, as SMSs go over the mobile network itself, not data/WiFI.