Finally solved this!
So from Mikrotik perspective, everything was set up properly. You might need IGMP proxy for some devices, but no need for PIM (some suggested that IGMP is not enough, even though every guide says it uses IGMP), just a simple IGMP-Proxy setup will do.
I have switched from avahi to this mdns reflector:
https://github.com/kennylevinsen/mdns-repeater
I don’t know what was the problem with avahi, because it kinda worked, Google Chromecast devices and Apple related stuffs as I said earlier worked correctly, but some services won’t. That’s why I never thought that the mDNS reflector is not working correctly, because some things worked anyways and also browsing mDNS traffic, everything reported correctly.
However switching mdns reflector, everything started to work immediately. Also discovery is faster now in every service.
There is a newer avahi-daemon version (8.0) but I did not have time to build it (not available through apt yet), it might solve these issues (but I don’t know why this happens).
Anyway thanks for everyone trying to help! It would be great if Mikrotik could implement its own mDNS reflector. Then this might worked for first try and you don’t need to mess around 3rd party services and devices.