For future reference, if anyone is looking for something similar:
I ended up buying a XPPen Artist Pro 12. It has a screen and provides so far a really clean sculpting experience. I got it for 220€ or so during the summer sales, it is a bit pricier otherwise. The size is perfect for sculpting in a relax position on a sofa or a chair.
When I sculpt, I usually first block out the shape with metaballs, and then merge them and go in sculpting. This is a process where quick iteration is nice, and which, with a regular setup, involves a lot of keyboard shortcuts. Unfortunately, the tablet only provides 8 buttons + a roller, which wasn’t enough for every action I typically use. I thus went with a mix between those buttons and some digital ones for reasonable iteration speed.
The buttons of the tablet I assigned first to the most essential and context-independent actions: rotating the view, moving the view, saving, ctrl+z. Then, the other remaining buttons I assigned to invoke the quick favourites, as well as some context-dependent pie wheels (provided by the addon of the same name). Quick favourites was especially a godsend here, because it allows you to pop a small menu with options defined by you, where you only have to click which actions you want to perform. In the modelling context, my quick favourites contain selecting, translating, rotating, scaling, adding an object, deleting, and duplicating. After some hours I found that I started memorizing which actions were where in the quick favourites menu, meaning the overhead compared to what I’d have with a keyboard was pretty small. The pie wheels also help, especially for quickly switching brushes. Those wheels are sadly not easy to customize, which is a bit frustrating.
In the end with this setup, I can sculpt pretty comfortably with no other tool than the graphics tablet (connected to my laptop of course). No keyboard or mouse is involved. I am probably in the end a bit slower than I’d be by using a regular setup, but the comfort of being able to sculpt with only the tablet and no other controller is well worth it. The tablet being a form of external display, you can also sculpt on it while having your references on the laptop’s screen, which is also really handy.