Agreed on the awkwardness of running into other clients. I suppose that's one positive of virtual sessions? (which I'm still doing--hoping to be back in person soon!) I was particularly bothered once when I saw my former marriage counselor hug someone, as to my knowledge, he didn't allow hugs. Also, when I was dealing with some erotic (and paternal) transference, and he walked out a late teens/early 20s girl who was dressed a bit provocatively. And another time when he greeted a client in the lobby by touching his knee.

Anyway, I'd bring it up with your therapist. That sounds especially awkward, what happened in the waiting room with the other client.