Construction costs are currently skyrocketing

One must also consider that during the DIY work, the loan is already being serviced as a rule, but one still lives in a rental.
That means, in addition to a month of DIY work, there are also 800, 1,000 or 1,500 EUR rent + additional costs to pay.

My tiler has tiled the kitchen (17m²), hallway (12m²), upstairs bathroom (10m², barrier-free shower) and the ground floor WC (2.5m²) in 2 weeks and is still not finished. Grouting, silicone and bathtub still need to be done. He has worked 10 days so far, 8-9 hours each day.
For an amateur, you can roughly estimate double (semi-professional, who has tiled a few times before) to four times (absolute beginner, mixing tile adhesive for the first time) the time. Besides work and family, I can manage to free up at best 25-30 hours per week, most of them on Saturdays and Sundays.
So for the tiling alone, I would have needed at least 10 weeks. That would have been 2.5 months’ rent just in my case, so the tiler would almost be "a bargain"...

DIY saves money especially when you do it while already living in the house or when you live rent-free.
In all other cases, you have to calculate very carefully; as a rule, it is not worthwhile or you save much less than you think.

Above all, one should not underestimate how much it takes out of you to work on the interior finishing every spare second next to your job for months or even years. After 1-2 rooms of drywall, you simply get fed up... but there are still 7 more rooms to go ;)

That's all true, but you can already sacrifice (approximately) your annual vacation two or three times for personal work. You can then work hard for days or weeks. Quite a lot can be done then. You work long days, the ratio of output to setup time improves, you are in the flow, etc. You (hopefully) don't go on vacation during or shortly after the house construction anyway.

My tiler has now been working for 2 weeks and is still not finished. Slope screed, shower waterproofing, facing walls done, sanding the floor, primers,... are taking quite a while. The actual tiling, I believe, is the smaller part. Although, of course, you can avoid some problems here. If you install it yourself, then there is just a shower with a low tray. That is less work and above all, there is less chance of making mistakes.

That's all true, but you can sacrifice your annual leave (almost) two or three times for DIY work.
You can then work hard for days or weeks. A lot can be done that way.
You work long days, the ratio of output to setup time gets better, you're in the flow, etc.

You (hopefully) don't go on vacation during or shortly after the house construction.

You might be "in the flow" when tiling after about 100m².
That means in the last room you look and say "Wow, that really looks professional now." Then you go to the first room and think "Oh God. I should actually redo everything now that I can do it properly."

Sure, DIY work is possible. But you have to be aware that months or years pass before everything is finished and you live on a construction site for that long.
The family has to cope with that first.

On the topic of tiling.... we recently did it ourselves in two basement rooms. Unfortunately, the substrate was not completely even and we also used very cheap tiles. I am actually quite satisfied with the result in the second room, but I consider tiling to be a DIY task that is really more for very, very skilled amateurs. It is not something you can quickly learn like drywall, painting, or laying laminate. Maybe in a utility room where it just goes straight ahead. But on walls, even the smallest difficulties quickly make it complicated, and you don’t have unlimited attempts. I am totally pro do-it-yourself, but I really exclude tiling from that.

Our energy consultant for KfW70EE renovation is charging 9,998€, which is 2€ below the maximum amount subsidized at 50%.

I have no values for individual measures.
As far as I know, KfW funding is only available for KfW85 anymore.