I remember once bringing up the fact that I had seen the next client to my therapist once and thankfully she understood how it felt for me. She then asked me a question that really made me see it in a whole new light and feel much better, she said

Do you not like your friends having other friendships?

She wasnt saying she was my friend but making the comparison and
I realised how that doesn't bother me- if my friends have other friends- and I asked myself why, and realised it was because i knew that it didn't take away from the unique relationship my friends and I have together. Therefore, why is it a problem that my therapist has other clients? It doesnt change the relationship we have. Remembering that helps me.

I know you know logically that if your therapist didnt have any other clients he wouldnt be a therapist- or else a pretty bad one to not have clients but it sounds like you felt insignificant when you seen this other client and began to compare yourself to her and I know how hard that is