Is it possible to effectively insulate the basement floor afterwards?

From an energy perspective, I wouldn’t worry too much about the thermal bridge. All additional measures to reduce this bridge would not be cost-effective.

Basement floor insulation is actually not trivial. From below, it is purely an energy-efficient solution. From a construction point of view regarding workload and foundations, I would think carefully about it.
Is the basement intended to be used for living purposes? Daylight? If not, then ceiling insulation of the basement is definitely the much easier solution.

Insulating strip foundations from the outside as shown is also no picnic, purely structurally.

Thank you for the tips. We want to use half of the rooms in the basement for living purposes (guest room, hobby room, etc.). Hence the idea to increase the ceiling height. If we can actually implement that (after consultation with the structural engineer), the question would be to what extent it can be insulated sensibly. Actually, it would be much more important than insulation to think about possible groundwater pressure. Well, on the one hand, there have apparently never been problems here, but you never know what nature might do in 10-20 years. Maybe I am just worrying unnecessarily and it would be completely sufficient to simply insulate the basement walls (without the foundation).

(Die Kellerwände sind an manchen Stellen weiß, sandig).

I would think carefully about the project. What is the current ceiling height in the basement? If the basement rooms are to be approved as living space, are there sufficient window areas? The whole thing will easily cost 40k, you could already build a small above-ground extension for that.

The room height is now about 2.15m. Another 20-30cm would be ideal. [Lochthöfe] will then be made. The architect is currently doing the drawings.

I would personally insulate the basement walls and leave the floor as it is.... then officially keep the rooms as [Nutzkeller]. A "living space basement" also involves certain requirements such as an emergency exit, etc.

Half of the rooms in the basement we want to use for residential purposes (guest room, hobby room..)

The room height is now about 2.15m. Another 20-30cm would be ideal. Light wells will then be made.

And you and your guests, you are all over 2m tall, which is why you always have to walk stooped? If the money has to be spent, do it by taking out the floor, but guests will probably rather go to sleep in the guest room in the basement and there the room height is probably secondary. And if your hobby is not exactly basketball or jump rope, 2.15 ceiling height should not bother there either.

Properly seal and cover the basement floor from the inside. Getting a warm basement floor in an existing building is not easy or rather getting it warm is, but so that nothing gets wet. There are also a few discussions about this here. There are several approaches, depending on religion.