I really would not recommend Azure unless you are going for an all-Microsoft, all-the-time strategy. Their hosted SQL Server offerings have actually been really good, and IMO is one of the best parts of the platform.

Would love to hear more about your opinions on the first part.

(We've used Azure for 3 years or so, AWS for longer).

Azure's USP is basically the deep integration into the MS ecosystem at all points. Azure is relentlessly promoted to every MS technical professional through all of the learning channels (and MS developer outreach is the best), Azure is integrated into the excellent developer experience of .NET and Visual Studio, hosted SQL Server on Azure is really nice (doubly so because it avoid the licensing quagmire), Azure with PowerShell is a fantastic CLI experience, etc. etc. Lots of reasons to love Azure if you are an MS specialist.

If you are outside the MS ecosystem, then you aren't getting much of that. For you, Azure is a less mature AWS with less support by and for your ecosystem. The situation with hosted MySQL on Azure is one example, but it is a two-way street: Microsoft loves it's own stack more, and folks outside the MS ecosystem love Azure less, partly because AWS is already the established default.

I could list papercuts and issues that I have had with Azure itself, but in each case I'm pretty sure or certain that AWS has had equivalent issues earlier in it's life, so it feels a bit unfair to do that.

I just met an azure representative in a event and they said managed mysql is in private beta right now. It will take them around 3 months to get it out if it. Even I'm waiting for it

That is great news as I'm probably going to use it in a large project that will start in a few months...

While not Microsoft offerings, there are some options available: my company Aiven (https://aiven.io/postgresql) offers managed PostgreSQL service on Azure as well. ElephantSQL (https://www.elephantsql.com/) is an another provider with hosted Postgres on Azure.