Unless you are facing extreme variability (changes) in your workload (i.e., growing by 20% per week or something like that), you should probably stay where you are. There's absolutely nothing wrong with stable, predictable organic growth.
"Microwave ovens can solve pretty much everything that Plato and Socrates does".
You need to frame your problem better. You can run Postgres _in_ AWS or Azure.
Both are platforms capable of storing data and running software using this data.
AWS, Azure as well as Postgres offer auth, queues, triggers, functions, document and table storage, and so on.
Yes, you can run Postgres on Azure; and you can run Azure on Azure, or Azure on your own bare metal, or Azure on VMs. I'm pretty sure it'd be possible to get Azure running on Postgres.