Unable to add HomeKit Bridge into Homekit across two LANs

Hi all,
complete newbie here when it comes to HA and I know just very basics about networks.
I searched for the topic here, but there is no applicable solution and it seems I have a little different situation going on. At least to my understanding.

THE SITUATION:
I have two LAN networks on different floors, each with its own Mikrotik router and separate internet/WAN connection. A separate apartment on each floor. These two LANs (one 192.168.0.0, second 192.168.1.0) are cable-connected together with ip/routes. No VLANs or any other segmentation yet.
I am perfectly able to ping or access any device from one LAN to another. Good starting point I’d say.
I need to automate some heating stuff and want to control some devices via Homekit, just to make it simple for the users.
So far, everything went smoothly when trying to set it up under one, let’s say 192.168.0.0, network (first apartment and boiler room).

The PROBLEM is, when I run HA on RPi on network 192.168.0.0, set up a HomeKit Bridge, and want it to add as an accessory bridge to HomeKit under the second (192.168.1.0) network/apartment, the HomeKit won’t find the Bridge and fails the procedure. I managed to add it only when physically moving the iPhone I am working with to the first LAN, but then still ended with NO RESPONSE on the added accessories, because the AppleTV that is running the HomeKit is still on the second LAN (and has to stay there).
I ran through a lot of posts here and there, but after reading about the mDNS repeater (not supported by Mikrotik), tried a couple of NAT rules, with no success.
What is weird - I can use AirPlay without a problem not only under one LAN, but even from one to the other (I am even able to see what my brother is watching on his TV down there :smiley: - yeah, I have to fix this later…), but not able to add the HomeKit Bridge to the HomeKit.

Any advice for a dummy like me on how to solve this?
Thank you!