You are correct. How would you distill this in to a handful of elements akin this submission?
Examples of things to consider: zero trust, multi tenancy, permission structures, user data classification (for GDPR removal/extraction requests).
As a European, GDPR has far reaching consequences that may even dictate what other services you rely on. I.e. can you use that SaaS service for your product when it's located outside of the EU/EEC?