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On a related question, not every notebook has all navigation keys as dedicated keys. When using go AI software, which navigation keys are needed frequently? Arrows keys? Pos1 and End? PageUp and PageDown? Is a mouse needed or will any touchpad do?
There are two different phases in my use of Lizzie and KataGo. First analyse the whole game, which takes about 90 minutes at 7000 visits per move. Then save the resulting SGF file which contains the analysed results so that it can be reviewed, also using Lizzie and KataGo. (Bad things happen if you analyse with LeelaZero and then try to review with KataGo, or vice versa.)
Lizzie has several single-key commands, but none that should be a problem on a laptop. For example: Up, Down, Left and Right arrow to move through variations; '.' to switch territory shading off and on, 'a' to start an analysis run, Space to switch analysis on and off at the current point in the game and Ctrl-1 or Ctrl-2 to switch between the two engines, which are LeelaZero and KataGo. PageUp and PageDown go forward or back 10 moves, but you can do without them if they are inconvenient on a laptop.
A mouse is used to select Lizzie's menu items and to move through the graph of results to focus on blunders etc. It is also useful to move the cursor off the board display during analysis, otherwise Lizzie thinks you only want to see the results of a move at the point under the cursor. As others have said, a plug-in USB mouse would be cheap and easy to carry around.
I have briefly used q5Go instead of Lizzie. From memory, it uses more mouse movements and fewer single-key commands than Lizzie, and also updates the screen less often. Indeed, Lizzie updates the screen rather manically.
It feels likely that a German-language installation would be little or no different to an English one, but you should be the expert there.
Whether you buy a laptop or a desktop really depends on your expected usage. Do you want to perform analysis at tournaments or in a summer house (Kleingartenhaeuschen)? If so, buy a laptop. If not, buy a desktop. In my experience, a desktop is likely to be better value, longer-lasting and more upgradeable. Your mileage may vary.
Here is an English proverb for you: There's nothing certain, save death and taxes.