Exclude tradesman based on his Google profile?

Whoever is working on MyHammer as a craftsman is not cream of the crop

I would also be interested to know if that is really consistently the case?
I have actually had good experiences with it, although that was already 10 years ago. Surely there are many "we can do everything, but not so well companies" included, but that does not mean that there are no good companies among them. Thanks to the rating system and the prior contact, you can filter quite well.
Certainly, due to the construction boom lately, the cream of the crop is probably already well supplied with orders anyway, so they do not necessarily need to look for MyHammer.
But there are also the "decent" craftsmen who maybe just do not get the big contracts.
Especially for smaller things like the work described by the OP, it will very likely be hard to find a larger established craft business.
For such things MyHammer is actually predestined.

We have the unpopular tender to install a washbasin and sink, whereby we would like to provide the material ourselves (except for fastening materials).

For that job I wouldn’t hesitate to hire the craftsman, but if you have a weird gut feeling, check again on the well-known classifieds portal. There you can often find all-round craftsmen advertising their services.

1000€ for that seems quite steep, or am I naive?

No, that is too much and probably a defensive offer.

Anyone working as a craftsman on MyHammer is not the cream of the crop

I have to disagree with you. A large part of the "normal" craftsmen are also active on platforms. Some of them are even large companies (30-40 employees). Of course, there are also many duds, that is probably true.

Unfortunately not yet. We have the unpopular tender to install a washbasin and washbasin, whereby we would like to provide the material ourselves (except for the fastening material).
I had also inquired with a craftsman (whom we know is good) about a complete service, but they wanted to charge 1000€ for it and have so far not been able to answer my question about exactly what is included in the price. Basically, we only want to have 2 narrow "shelves" mounted on the long wall in the guest bathroom, and the washbasin should be installed on the top one (cutting out something from one of the boards for the connections).
I find 1000€ quite steep for that, or am I naive?

Depending on how large the washbasin and vanity unit are and what kind of wall there is (drywall) etc., it is usually a day's work with 2 people (with large washbasins you need 2 colleagues).

1 day of installation, travel, silicone joints, small parts, etc.

1000 including taxes is quite accurate.

So, a few years ago I found my tiler through the well-known portal. A one-man business. He did excellent work and took me along to a current construction site beforehand so I could decide for or against stainless steel strips.

Now, to be honest, you have a very unpopular job to assign. For many companies, it’s not worth installing non-provided materials or accepting very small jobs. Hence probably the €1000 offer.

And seriously, you could do that yourself too. He, as a craftsman, probably does it well enough.

For many companies, it is not worthwhile to install material that has not been provided, ...

Do I understand correctly that craftsmen earn not only from the service but also from the material prices? I ask because so far I assumed that craftsmen use better materials and that is why it is more expensive than the material from the hardware store.

Of course, the craftsmen also earn money from the material. They cannot pass it on 1:1. They usually use better material than the hardware store. But why is the hardware store allowed to earn money on the material and the craftsmen not?