Link: https://en.wikipedia.org/wiki/B_Corporation_(certification)

There are a few EU seals on products that guide my shopping, the Eco-label the Organic and the certified origin for regional products. Should there be also one that certified social good practices by companies?

The B corporation is a good idea, but it's also an US private seal involved in a few polemics.. getting the seal implies paying fees to a US organization.

Isn't there already enough labels?

And like you said: who will bear the cost of that nth label?

In a way the best is to have strong laws that ensure EU companies have a high degree of social rights.. but, it would still be cool to award outstanding companies.

Imo the B corp certification is not needed at all.
For example German-speaking countries have special types of entity for non-profit companies (gUG and gGmbH) and I'm pretty sure other European countries have a comparable legal entity too.

The thing is, we're in a common market, EU-wide recognizable seals are always better. European brands already use the B corp one, so there's definitely a market for it.

No.
B Corp is nothing but a money making exercise.
The B stands for Bullshit.