Is engineered wood flooring unsuitable for bedrooms?

I would orient myself based on whether the floor is approved for underfloor heating or not. 0.15 m²K/W is, I believe, the limit that someone came up with for that. Less is better. In the end, you need a few degrees higher flow temperature throughout the entire house. The "worst" room determines the flow temperature. The ground floor will be throttled more, the upper floor/parquet rooms get full flow. With gas it doesn't matter, with a heat pump it might cost about 50€ more per year.

If you heat with a heat pump, I would plan the underfloor heating so that in rooms with parquet it is laid a bit more tightly. In critical rooms with parquet (small but high temperature desired, e.g. an office/children’s room) you could also bring a few meters of the underfloor heating into the wall, then the issue is completely resolved. Later do the hydraulic balancing yourself / remove all thermostats or keep them fully open permanently and control the heating exclusively centrally to keep the flow temperature as low as possible. Always heat the upper floor corridor.

Definitely bond it. That also somewhat reduces the imbalance regarding heat transfer capability between the ground floor (tiles = very good) and parquet (less good).

Already said: The seller has no idea and unfortunately it will not get colder at night.

I would orient myself on whether the floor is approved for underfloor heating or not. 0.15m²K/W is, I believe, the limit someone came up with for that. Less is better. In the end, you need a few degrees higher supply temperature throughout the house. The "worst" room determines the supply temperature. The ground floor will be throttled more, the upper floor/parquet rooms get full flow. With gas it doesn't matter, with a heat pump it might cost about €50 more per year.

If you heat with a heat pump, I would plan the underfloor heating so that it is laid a bit closer in rooms with parquet. In critical rooms with parquet (small but high temperature desired, e.g. an office/children's room), you could also install a few meters of underfloor heating into the wall, then the issue is completely resolved. Later, do the hydraulic balancing yourself/remove all thermostats or leave them fully open permanently and control the heating exclusively centrally to keep the supply temperature as low as possible. Always heat the upper floor hallway.

Definitely glue it down. This also reduces the imbalance regarding heat dissipation capability between the ground floor (tiles = very good) and parquet (less good) a bit.

Already said: The seller has no idea and unfortunately it won't get any colder at night

I’ll ask again, thanks for the hint. We heat with a gas condensing boiler. The underfloor heating is already installed, so we no longer have any influence on how close the pipes are laid. Yes, we definitely want to glue it down.

One more thing... would you notice the height difference (even with a rail) from the hallway (finished parquet 14mm + ~1mm adhesive) to the bathroom (10 mm tile + x mm adhesive), or does it end up roughly the same height? We have porcelain stoneware as the floor tile 60 x 60 cm.

I'll ask again

Get the datasheet/manufacturer information for the coating.

Another thing... would you notice the height difference (even with a rail) from the hallway (finished parquet 14mm + ~1mm adhesive) to the bathroom (10 mm tile + x mm adhesive) or does it end up roughly the same height? We have porcelain stoneware as floor tiles 60 x 60 cm.

Our tiler wanted to know the height of the parquet and said that if necessary he would slightly raise the tiles (more adhesive or something?). We don't notice any height difference, but I didn't ask further whether the raising was really necessary anywhere.

If you have a good tiler, he will compensate the 5mm with adhesive in the last 2 rows. You won't see or notice it.