Replace a standard washbasin with a washstand system myself?

Depends: there are production countries that do not have our standard.
Is the price for Ikea?
For our standard sanitary, we could choose between two washbasin variants (countertop and wall-mounted). We then chose the countertop and had a 160 cm panel (EL) installed on site with the plumber for 50€, also got the supports ourselves. Later we installed Godmorgon ourselves as a base cabinet.
So I would always consider Plan B and C. Pinterest only shows what you are looking for ;) although there is much, much more.

Retrofitting washbasin from Villeroy and Boch.

I haven't read the entire thread, but I can still recommend asking your kitchen dealer about the washbasins; they also install everything and provide an installation sketch (like when buying a kitchen), so that the sanitary connections can be laid accordingly right away. That was our alternative to the standard from the general contractor.

The standard is a small Geberit washbasin, we ourselves would like to retrofit a washstand from Villeroy and Boch.

Kitchen dealer for a washbasin in the bathroom? That’s new to me :-D