Ground floor hallway push-button switch -> Hue Motion Sensor

Exactly, light bulbs and sensor via the bridge. The switches shouldn't really be removed.

I just had the idea to take a flat "lampshade" and place a short Hue Strip behind it - virtually invisible - thus having a switchable LED light source. You could control the ceiling lamp and the stair lamp individually via Alexa. You would only need a constant "ON". Which, as you say, could probably be done with the bridging.

Exactly, light bulbs and sensor via the bridge. The switches shouldn’t really be removed.

I just had the idea to take a flat "lampshade" and place a short Hue strip behind it - virtually invisible - so that a switchable LED light source would be available. You could control the ceiling lamp and the stair lamp separately via Alexa. You would just need to keep it permanently "ON". Which you - as you say - could probably do by bridging.

The Hue strip has a ridiculously long power cable though. I think I’m imagining something wrong with it. You can just use the regular Hue bulbs for that, right? There are also Hue wall lights (the look has to be right, of course) or you can just use ones with sockets and put Hue bulbs in them.

Ah of course... you are my hero...

Hue also comes as wall lamps... ready to use. I always used the finished flat LED lamps that have a fixed light source built in... basically as non-Hue lamps.
Only the continuous "ON" bridging would remain.

One could insert a profile into the now existing vertical slot and glue an [Hue Strip] inside it. Now only the wiring needs to be elegantly concealed. In other words, the power supply should be flush-mounted, possibly equipped with some kind of maintenance flap. The strip connection is located at the bottom at stair level or beneath the stringer of the short side of the stairs.

Anyone have an idea?

Unfortunately, there isn’t much selection in terms of aesthetics, but the ones I saw were actually fine.

If only the two switches are involved, it’s a simple matter to change it. You can also install Hue switches. They would still be switchable then.

I did that at my neighbor’s place. However, only afterwards to make sure it’s really straight. You can simply get a U-profile including frosted glass. At one spot behind the slot, a bit deeper/wider so that all cables including the transformer fit in. From there, in the empty conduit under the steps into an outlet.

Right, the selection isn’t that great... and usually it’s more like an outdoor lamp or extremely expensive, e.g. the "Liane".

Currently there are no switches for the two stair lamps, only the cable to the switch cabinet.

I’m exactly thinking of such a U-profile, with the frosted glass, so that the light shines continuously and you don’t see the individual LEDs.

With a deeper/wider profile behind the slot it will certainly be critical, it’s only a 17.5 cm exterior wall, with [WDVS].
You mean in the last sentence, the cable "plug -> connection transformer" in the empty conduit below the step. The plug would then stick out a few cm from the wall and go directly into the box? Should I imagine it like that?