Which type of funding should I choose? KfW, BAFA, tax?

May I ask how many cm of facade insulation you installed and what material (plus thickness) your exterior walls are made of?

Sure. The house has 36.5 cm walls (mainly pumice with clinker without an air gap). The plan was for 10 cm XPS insulation WLG 28 for the basement (a room partially below ground level) and perimeter insulation. Additionally, 12 cm Resol insulation WLG 22 (otherwise the roof would have had to be extended at the gable ends). That was sufficient for KfW 55. In the end, the aforementioned insulation was used on the gable ends. However, I used 12 cm PUR WLG 26 for the basement and perimeter insulation. On the non-gable walls, 16 cm Resol insulation was applied.

Interesting! We have:

Exterior walls 2x11.5cm + 6 cm air gap + existing 8cm ETICS from 1999
Due to the low basement ceiling height (partly only 1.90) only 8cm Isover Topdec WLG 31
Roof is new with U-value 0.14
Triple glazing windows Ug value 0.6 and U-value 0.94.

This only results in KfW 100 according to the thermal protection certificate (or KfW 90.5, if you want to be precise :))

Exterior walls 2x11.5cm + 6 cm air gap in between + existing 8cm ETICS from 1999

Make sure to blow out the air layer! The increase in thermal insulation here is unbeatable in terms of price/performance. But much more importantly: without a filled air layer, the preceding ETICS is almost ineffective, or with a closed air layer, significantly less effective.

What would need to be different to achieve KfW55?

KfW 55 imposes very high requirements on transmission heat loss / building envelope and practically allows no gaps here. If KfW, then I would recommend KfW 70 as EE - renewable energy class with heat pump. That gives an extra 5%. Then you should have it determined beforehand that it is a "worst performing building," meaning energy class H, which should fit your description. - That gives another 10% repayment subsidy. (WPB bonus is only available for KfW70 or better.) If the conditions are met, it is actually not so important to achieve KfW55 anymore, because the extra effort usually does not pay off cost-wise.

KfW 70 specifies a maximum Ht' (specific transmission heat losses = quality of the building envelope) of 85% of the reference value for new buildings. That is already a tough target for existing buildings. At least 16 cm WLG032 facade insulation, 12 cm WLG035 basement ceiling, and 30 cm WLG032 roof insulation, as well as windows with Uf < 0.95, specific thermal bridge verification, and possibly a blower door test to ensure building airtightness are probably required.

Apply for the KfW 70EE with WPB bonus as a loan with repayment subsidy for facade insulation, windows, and basement ceiling.

Apply for the heating system itself through BAFA with replacement bonus for the old gas/oil heating (hopefully over 20 years old) including ancillary measures like underfloor heating.

For the floor construction with underfloor heating, you best also need insulation on top. Therefore, in existing buildings, I would go for a dry construction system. That has only 25 mm build-up height with 16 mm pipes (do not choose thinner!, just google "flow30" - not as dogma, just as a guideline) + 2 cm dry screed (there are also options as XPS without the need for dry screed on top) and you can still lay WLG022 PIR insulation underneath.

You have to see about the roof. If it meets the KfW requirements with the new internal insulation, you can also claim the material costs here through KfW; tax deduction is not possible for your own work.

All of this must be calculated by the energy consultant who handles the application and support for the subsidy. But that would be the target value I would aim for. These are maximum repayment subsidies with feasible effort.

Make sure to blow out the air layer! The increase in thermal insulation here is unbeatable in terms of price/performance. But much more importantly: without a filled air layer, the upstream ETICS is almost ineffective or significantly less effective with a closed air layer.

Yes, that's still somehow on the to-do list (but not for right now). In the construction documents of the house (from 1936) it looked like a monolithic wall. When the structural builders made the openings for the patio door, etc., they realized it was built with a double shell. That also cost us quite a bit more steel...

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Apply for the KfW 70EE with WPB bonus as a loan with repayment grant for facade insulation, windows, and basement ceiling.

Apply for the heating itself through BAFA with an exchange bonus for the old gas/oil heating (hopefully over 20 years old) including surrounding measures such as the underfloor heating.
[...]

Is this even still possible currently? I believe I read that in addition to the KfW funding, the heating system can no longer be subsidized through BAFA.

But then the question arises again: If I now, for example, do not get funding for roof insulation through KfW, can I really still get it funded somehow differently (BAFA, tax relief)?

[...]
For the floor structure with underfloor heating, you ideally also need insulation on top. Therefore, I would recommend a dry construction system for existing buildings. With 16mm pipes (don't choose thinner!, google "flow30" – not as a dogma, just as a guideline) it only has a build-up height of 25mm + 2 cm dry screed (also available as XPS without the necessary dry screed on top) and you can lay WLG022 PIR insulation underneath.
[...]

I wanted to use the thin-layer system from Schlüter here. I have absolutely no experience with dry screed, nor anyone in my circle of acquaintances who uses it.