It's both. They have a handle below the screen precisely for this reason. [1] You can grab it and press the buttons below/tap the lower part of the screen above with your thumb. This seems much more reasonable and pragmatic than the sci-fi looking mockup they originally presented. [2] Although my understanding is that it's probably not a huge problem, because Soyuz introduced the stick to push the buttons only in its later variants.
Also, judging from the photos, they seem to have their button covers supported by the frame. In 2003, there was an incident when a cosmonaut inadvertently fired RCS thrusters on the Soyuz attached to the station, simultaneously pushing several buttons with his foot while loading the spacecraft with cargo to be returned to Earth, crushing the protective caps that were pressing against the (relatively flimsy) case. The thrusters fired for quite some time until a ground operator noticed it and turned them off remotely. After that, the covers in Soyuz were redesigned to press against the frame. Seems like that incident has been learned from in Crew Dragon as well.
I would imagine they would have control lockouts as well. Not something super complicated/time consuming to disengage, but something to prefect that exact scenario from happening.
Yes, the lockouts were in place during that incident too, but for several good reasons they are non-modal - you have to hold two buttons at the same time to trigger some critical operations like manual RCS controls. Which is exactly what happened, so the confirmation procedure had to be changed as well.
Also, judging from the photos, they seem to have their button covers supported by the frame. In 2003, there was an incident when a cosmonaut inadvertently fired RCS thrusters on the Soyuz attached to the station, simultaneously pushing several buttons with his foot while loading the spacecraft with cargo to be returned to Earth, crushing the protective caps that were pressing against the (relatively flimsy) case. The thrusters fired for quite some time until a ground operator noticed it and turned them off remotely. After that, the covers in Soyuz were redesigned to press against the frame. Seems like that incident has been learned from in Crew Dragon as well.
[1] https://imgur.com/KyAaQS0
[2] https://imgur.com/pTYfAew