Well I can't speak to Heer tank crews.... but Australian Army tank crews have historically filled their "downtime" in any number of ways.

Maintenance is probably a bigger time-killer than you'd think, especially depending on the theatre topography - settings where dust/sand is prominent doubly so, as sand tends to do an outstanding job of ruining electronics or even mechanical components. But remembering that logistics can struggle to keep up with fast moving armoured columns in any wartime environment, this can mean that spares as well as consumables might appear sporadically rather than "all at once".

Activities from external maintenance (track pins, track pads, track link, roadwheels etc would all need to be checked and replaced), to checking the levels and integrity of POL, testing and maintenance of communications gear, replenishing food, water, and ammunition as well as administrative preparations such as orders groups, dismounted patrols or laying out Observation Posts are all a host of duties that Armoured soldiers certainly the British or Australian Armies (the latter being my area of knowledge) were expected to fulfil in their "downtime". Whilst the German Army was functionally different, there are only so many ways to administer a functional armoured unit at a sub-unit level, any of which would be plausible for your novel or novella.

Other less formal activities would plausibly include, being frank, anything ranging from perfunctory activities like sleeping, and eating to more remarkable activities such as minor pranks, gambling, writing to and reading letters from home, (re)reading newspapers (that would almost certainly be old) or even attending various individual biological imperatives.

These are of course, largely dictated by the amount of downtime we're talking about, position of the friendly unit, the likelihood of enemy action or threat, and the needs of the unit - it would be, for example, unlikely for a vehicle commander to stroll off and read a letter from his girlfriend from home and have some 'alone time' if one of his radios needed replacing with a spare that had just arrived... there would also be certain maintenance, administrative or personal activities that would either be modified in their execution or foregone entirely dependent upon the tactical need for sound and light discipline.

Again, for the Australians in combat roles (including armoured ones) culturally when in an operational context, the focus has always been maintaining the fighting platform as a priority, with sleep, food or other personal administrative requirements coming next, with personal entertainment coming in last.

Hopefully that helps.

Probably the same way as any other soldier would.

That said, if the war s that slow, assuming there are no major inhibiting issue such as fuel or ammo (so not late war Germany), you can expect that they'll be taking advantage of the slow time and pull as much maintenance as possible on the tank, and also conducting training evolutions. Just because the war is slow doesn't mean that you stop soldiering.