Construction supervision via Bauherren-Schutzbund, Association of Private Builders, TÜV, DEKRA, independent expert surveyor, or "xyz"...?

When it comes to the person commissioned with supervision limiting their liability to their fee, it probably means that they are only liable for what they could have seen.

What they could have seen is limited to the fixed appointments agreed upon in advance with the supervisor.
TÜV and DEKRA work here with a multi-point (five?) plan, meaning five appointments when someone comes by and inspects the acceptance of certain phases and parts (e.g., after the installation of perimeter insulation of the basement).

Defects that occur between two appointments and are then, for example, "covered over" or otherwise concealed cannot, of course, be discovered by the expert and thus they are not liable for these.

A fixed fee is agreed upon/prescribed for these five appointments plus travel costs (charged per km).

A gentleman from the Bauherren-Schutzbund (Bauherren-Schutzbund) told me that he would come by for nine appointments. Billing is according to actual hours worked at €85/hour (uniform rate at the Bauherren-Schutzbund).
However, you must be a member there for €100?/year.
This one gentleman could also carry out the Kfw55 inspections (additional/ combined appointments).

If I want, the guy can also come to the construction site every day and check, €85/hour as mentioned.

With an architect, there is performance phase 8 construction supervision. A fixed fee (according to HOAI or lower if negotiated) is due for this. Due to the flat-rate commission, the architect is correspondingly liable for all phases.
If you search for "architect performance phase 8," you will also find a lot about liability, especially regarding what is reasonable (finding defects and not needing to be on the construction site around the clock).

Liability is, however, relatively subjective, I presume. One person passes the buck to another. But I am not very knowledgeable legally.

In the end, in my opinion, the following is sensible:
- Ask the Bauherren-Schutzbund and possibly other associations how it works for them, what it would cost, and what is supervised
- Ask TÜV, DEKRA, and possibly others what it costs and what they supervise and whether it can possibly be expanded (five appointments seem too few to me, gut feeling)
- Look for an independent expert and ask what they recommend and what it costs or ask them what the same service costs that one of the above offers, or what a flat-rate supervision like with an architect costs
- Ask an architect what they charge for this performance phase

Ask, obtain offers, weigh options, decide, and possibly post here with reasons for decision-making.

Personally, I think if you build with an architect, you can also go through all phases.
If not (as it probably will be with us, building directly with the construction company with its own planning department at a fixed price, cheaper than all GUs so far), then I tend towards the gentleman from the Bauherren-Schutzbund.

phew, rummaged through and still no progress.... we planned with architects, who will now also take over the construction with his company and tender additional trades. The same question arises for me – an external expert would probably make sense, since rework would cost the architect money, so it wouldn’t be in his interest. On the other hand, as the construction supervisor, he is liable if something goes wrong? What is sensible now?

Since the architect belongs to the construction company, take an external supervisor as well. If the architect did not belong to the construction company, there are opinions that would still involve an external one and there are opinions (including mine) that would then consider the supposedly independent architect as the supervisor.

Since the architect belongs to the construction company, hire an external supervisor as well.
If the architect does not belong to the construction company, there are opinions that would still involve an external person and there are opinions (including mine) that would then consider the supposedly independent architect as the supervisor.

And ideally, the architect I commission is also an energy consultant and can be subsidized as a construction companion by the KFW?

Yes, but usually it is already possible with the general contractor or the construction company because they themselves also hire someone external to carry out the work (this has already been explained to me by various GCs/ construction people).

I am currently wondering if it is possible to commission two people with the supervision and bill this to the KfW Bank.
In other words, the GC/ construction company also does the KfW55 proof, corresponding checks, and efforts, which I bill to KfW at 50%.
To be on the safe side, I commission an external expert (e.g., from the Bauherren-Schutzbund) who is also supposed to carry out the KfW checks (additionally). Can I also bill this to KfW (assuming that the funding cap of the eligible amount is observed)?

Whether that makes sense or not is not the question here, but only whether double services can be billed to KfW.

Alternatively, I would have to revoke the KfW calculation from the construction company or I stipulate that they carry out the external assignment to the expert of my choice.

I am not the KfW expert here!
But I notice a flaw in your last post (at least to the best of my knowledge/reading)
1. the person who checks the energy efficiency from KfW55 onwards must not be economically connected to the construction company, and must be a certified energy advisor from a special list
2. invoices are not submitted to the KfW bank, but are settled with the approved and paid-in-advance repayment subsidy