That is not to say that this aspect alone justifies huge fees, but it does have significant value.
AWS RDS does not upgrade major or minor versions of Postgres or, as you mentioned, MySQL. In that case, they might patch update it. But these patch updates are easy to do yourself and does not take long to be reminded of in your ISMS and then subsequently carry out.
The purpose of this post is not to justify cloud hyperscalers versus European servers. It is actually a post on how to manage a highly regulated, compliant, and certified server setup yourself outside AWS because so many people just have their ISO certification on AWS infrastructure and once they got that they are never able to leave AWS again.
If you have no client demand and no real need to work on updating your infrastructure yourself, then you can go ahead and not go for an ISO 27001 certification and let AWS RDS update as it pleases. But if you operate a complex beast in a regulated industry such as employment law, finance, and such, then you get some more fun challenges and higher need for control.