Very wet windows overnight

Unfortunately, you forgot the attachment?

A lot of heating, as mentioned, is rather not possible because the heating system gets exhausted after a while and then has to "recharge" before it can heat again, so it often happens that the room cools down simply because it can no longer be heated.

That is also your main problem as already described. You can see the consequences on the windows. That is simple physics.

Heating and ventilating, only that will help. The moisture simply has to get outside.

All the heating and ventilation doesn't help at all if the windows are bad. You can't heat against cold panes and shouldn't do it either (energy-saving topic). If the windows are drafty and air is coming through, get the landlord involved. You can also measure the surface temperature of the pane (infrared device). If it is too low, the dew point is undershot and condensation forms.
You can also buy a cheap humidity display device.

Back then in our rental dump the same problem: the landlord came with the old routine of ventilating and heating, unfortunately the humidity was below 50%, usually around 42%, so no wrong tenant behavior there. The panes were soaking wet with puddles on the windowsill. The puddles were also in the frame, everything was happily molding. They were simply bad windows that were poorly installed.
Here in the house we have exactly the same heating and ventilation behavior and the panes fog up as well: but from outside!
Inside it’s completely dry.
If the place molds even though the indoor humidity is okay, rent reduction!

External links are prohibited according to the admin... , you say below 50% humidity, once this is reached you can continue to monitor.

Yep...off topic Elina...

As far as I have read, the OP doesn't know anything about the humidity yet. Measure first, then you can see further.