That sounds like DBA as a Service. No, we don't plan to support that in the near future. One thing that is definitely on our roadmap and may be relevant is BYOA (bring your own account) when hosts of the cluster are running in your AWS/Azure/GCP account, not ours.
About failed attempt of moving to MySQL. It was more than 10 years ago and I wasn't working at Yandex at that time but AFAIK the main problems were not around technical problems, they were organizational - not all members of the team agreed on moving to MySQL.
We had several kinds of stored logic in Oracle:
1. for logical consistency of data (i.e. when you store new message you should increment counter for folder, thread, etc.). It seems correct to have such logic in the database rather than in the application.
2. for common code (i.e. moving a message from one folder to another may be done from web backend, mobile backend, imap backend or pop3 backend). This kind of logic is easier to have in one place than in all backends.
3. some business logic (i.e. finding thread for a new incoming message was done in PL/SQL).
First type is still in the database. Some part of type 2 was moved to our abstraction library (that is used by all applications). Logic of thrird type was moved to our applications and it greatly reduced stored code size.
Hardware for Oracle and PostgreSQL are different. We used to have big boxes for Oracle with lots of memory, SSD disks and rigid economy of CPU (small number of very fast cores because Oracle is licenced per CPU cores). And that hardware was really efficiently used in consuming nearly all system resources (CPU, I/O, disk space and even network bandwidth).
For PostgreSQL we use commodity servers and right now they are not really efficiently balanced (i.e. on some hosts we don't have enough disk space but other resources are utilized ~30%). So we are working on improving that. But I can't tell you exact numbers of hosts for Oracle or PostgreSQL (which is actually ~x3 from Oracle hosts number :)).
We started our first production systems with 9.3. When we started migration process and until it ended we used 9.4. Right now all our production clusters are 9.5.
Nobody argues that Oracle is a very good database. But 3x more hardware and 10 man-years are an order of magnitude cheaper than Oracle licencies cost (even with maximum discount).
No, you are not right. In video (Q&A section in the end) you can hear that rewriting stored logic took a couple of weeks of one developer. Maybe a couple of month with good tests.
It took much more time to rewrite backends logic because of lots of legacy code in many applications without using abstraction libraries.