Formula fed baby, nipple for comfort?

I’m a first time mom and still making my way through motherhood one step at a time. My daughter is almost five months old. I wanted to breastfeed desperately, but between her tongue tie, refusal to latch after getting the tongue tie corrected, postpartum depression and just lack of knowledge and support for breastfeeding... it just wasn’t successful. So that’s my long winded way of saying she’s exclusively formula fed.

She also has in general refused every pacifier we have given her. We’ve tried multiple brands, and she doesn’t like any. Yet when she is worked up or trying to go to sleep, she makes a sucking face like she wants one. She refuses to take it, doesn’t want a bottle, and at my wits end to try to soothe her, I put my nipple in her mouth.

I’ve been dried up for months obviously so there’s no milk, but she instantly sucked like it was a pacifier and fell asleep within a few minutes. My question is... is this normal? Is this weird? Does anyone else have formula fed babies who just want their mamas boob for comfort? I just want to soothe my baby. I don’t want anyone to think I’m perverse for this. Just looking for solidarity and assurance that this is okay, I suppose!