Epilogue:
I have bought a small piece of Bal Rapid Mat, which is only 1mm thick. Used 4mm notched trowel and then matting on top.
This gave me an extra ~3mm height on a fairly stable even ground. Embedded the trim with adhesive and then tiled. Mad respect for tilers, as this was not easy! I thought this "small" project was DIYable, but I think that tiling an entire plain bathroom floor would have been easier.
Would I do this again, not sure... In case anyone is planing something similar here is what I learned:
- manual tile cutter works, but only straight lines and on a 45mx45mm tile the smallest piece you can cut is probably a third of it. Trying to cut smaller pieces just destroys the tile and leaves sharp edges (cut my hands twice...)
- having an angle grinder with the right disc handy would have been helpful
- subfloor preparation is absolutely key. If I were to do this again, I would've have probably started with a 3.6m plywood.. then the cement board with screws all the way through
- I used dark anthracite grout, and when everything was completely black, I panicked a bit and started cleaning too early. Which removed too much grouting, so now the grouting lines look a little sunken in
- keep some spare grout on the side (in an airtight container so it does not dry too fast). While you are sponging the tiles, you will eventually discover (or create) more holes and gaps, which you then can re-fill straight away
- work with lots of masking tape!
Anyway, it is done now and an acceptable result. I will still need to put some flex gap filler between the metal trim and the floor.

p.s. cleaning buckets and tools of adhesive and grouting is a real pain!