Should I tell the recruiter?

Okay so here’s the thing. I just got a call from company A and they are willing proceed. It’s a contract role. (Shitty pay, onsite 5 days blah blah not a great job)

Company B: Finished with the last round and the recruiter emailed that they will take the decision by next week. Good company and good pay (this is my first choice IF I GET IT)

Question is should I reach out to company B and say that I have an offer from Company A and maybe they might expedite or something?

I want to understand from recruiter and company perspective do they like candidates with multiple offers? Or maybe by informing them will it put me in a bad position?

What should I do? Just sit back and wait? Need suggestions