Floating vinyl flooring installation

we have 3 rooms + hallway on the upper floor

Rooms = 10, 12 and 15 sqm + 3 sqm hallway

Would there be any problems if we laid it continuously without transition strips?

Could someone also tell me what the finishing strips to the stairs are called?

It’s the same as in the picture above at our place too

Would there be problems if we laid it continuously without transition strips?

Unfortunately, I cannot say for sure. If it were me, I would lay it continuously.

We have laid it completely and continuously. Parador Modular One. The max. extension is, I believe, 12m x 20m - it's written on the packaging or something like that. That is the maximum area without an expansion joint, according to Parador. Work the design floor up to the stairs and seal the joint with silicone. We laid it with Acoustic Protect underneath instead of just a vapor barrier, it was repeatedly recommended as a secret tip.

The room size is no larger than 12x20m but there are several walls in between that we have to lay around.

So at the stairs, just lay it next to it and put a silicone joint, right?

In the hallway, we still have a distribution box for the underfloor heating, probably also lay next to it and seal with silicone.

So you would all lay the floor continuously without expansion joints?
We would then lay the floor over a total of 3 expansion joints in the screed.

Why did you lay acoustic protect underneath?
The floor already has integrated impact sound insulation.
I even read that it is completely wrong to lay two impact sound insulations, so one underneath plus the integrated one.

I think you should read the installation instructions for the floor. Quickly, I found the following about Modular One:

The carrier plate of the vinyl with HDF carrier plate and also the special carrier plate of Modular ONE is a wood-based material that, like natural wood, is subject to swelling or shrinking depending on climatic conditions. Therefore, the installed floor with HDF carrier plate requires an appropriate distance to all heavy objects (e.g., kitchens) and to all fixed components, such as walls, supports, radiator pipes, etc., called wall clearance or surrounding expansion joint. Furthermore, when exceeding a defined installation area, equally sized expansion joints must be observed. Insufficient wall clearance or spacing in the expansion joints is the most common installation error. This often only becomes noticeable in summer because the floor expands due to the increased humidity and temperature during the summer months. The expansion joint and the wall clearance should be at least 8 mm* (picture 3) for vinyl with HDF carrier plate and also for Modular ONE (special carrier plate), correspondingly more for larger areas (see section: Arrangement of expansion joints: room size larger than 8 x 12 m).

Even if the installed material only touches one spot in the room (is worked in), floating installed material can become pressed and warped. Frequent weak points are door frames, stair connections, radiator connections, and finishing rails.

Thanks

But I have another question.
If I use a silicone joint in the expansion joint on the stair transition

Silicone joints do work, and with tiles you also use a silicone joint as an expansion joint.

However, the floor in my shown picture was also installed by a professional company.

I am totally confused about what can or cannot be done now.