You are right. Are you actually seriously considering whether to go fully managed or self managed at this point? Pls go AWS route and thank me later :)
I didn't include labour costs, but the self-hosted tasks (set up of hardware, OS, DB, backup, monitoring, replacing a failed component which would be really unusual) are small compared to the labour costs of the DB generally (optimizing indices, moving data around for testing etc, restoring from a backup).