I am an adopted child – did my parents mess up?

I was adopted into a Jewish family at birth. Meaning that the legal arrangements were made before my birth and I was given to my parents basically right after my birth (they were literally in the delivery room with my bio-mom).

My parents raised me in Judaism as if I was born biologically from them – that is to say, I immediately got a bris, went into religious education, and had a bar mitzvah. For what it’s worth, I’m like 99% sure that the rabbi who performed my bris knew I was adopted.

*Now for the twist *– My biological mom had a Jewish mother, but she herself was baptized in the Baptist church

I have been doing readings on Jewish law in regards to adoption and i just want to make sure I wasn’t supposed to have converted first? I’m a little worried as I am both culturally and religiously Jewish and I want to make sure that I am recognized as a Jew by Jewish Law.