Screed on wooden floorboards over crawl space and more

I would bite the bullet and fill the crawl space, put in good insulation and that’s that. Everything else is long-term botch. From above it is warm and humid due to residential use, vinyl seals everything nicely and the moisture can then beautifully gnaw away the floorboards and beams from the cellar side together with fungi and woodworms.

So you have about 4 weeks until moving in and will only then find out what exactly is involved. From floor construction to walls, ceilings, heating, pipes, etc. If you are not actually the craftsman, have a month off, and have all the tools and helpers, then you can already start renovating a bit. If you are not, then stop these ideas immediately, because my craftsman is waiting for you, materials need to be chosen, delivered, and installed, and one trade can only be carried out when the other is finished. Maybe there is the option of a phased move, where you finish one or two rooms by then, specifically those that require little renovation. You will be overwhelmed by materials, problems, waiting times, sudden changes during the construction, etc. - don’t ruin your Christmas. Better to take it slow and thoughtful, so start from the bottom dry, that is to seal the crawl space if necessary. On wooden beams (if these are still really okay) you can then easily work with drywall, like OSB, floorboards, etc., no screed is needed there.

I don't know the circumstances, but I too would do a lot to avoid having to move in so hastily. As you have rightly recognized, a gas heating system is on the decline. However, the conversion to a heat pump needs to be well planned. It also helps ENORMOUSLY if you have installed as many underfloor heating systems as possible. Both are currently subsidized by the Bafa at about 45%. Including pretty much everything. Don't miss the opportunity - you don't want to do this once you've moved in.
In the process, you remove the [Thermie] from the roof, renovate it, and fully equip it with photovoltaics. The old system can perhaps be moved to the carport or similar. Otherwise, please prepare it in a way that allows the area occupied by it to be retrofitted and connected to the new system in five years.
If the last renovation was in '88, the electrical system and certainly quite a bit of the plumbing also need work. Also things you don't want to do after moving in. You can get part of the electrical work tax-free because it can be combined with the photovoltaic system. You can get part of the plumbing subsidized because it is necessary for the new heating system. (Of course, not the new toilet...)
A huge, unique opportunity is opening up to you. Don't sabotage it because you don't want to stay in the rental apartment for another six months (or whatever the reason for the rush is).