We've taken turns being bio and nonbio moms, and I will say that it takes a LOT of effort to overcome inherent baby preference for the lactating parent, especially if the lactating parent is also the one staying home with the kid(s). You just need to keep doggedly at it and during periods of favoritism just offer the nongestational parent for comfort whenever they're around, and don't take the favoritism seriously, even though your baby might be a complete and utter berk about it sometimes. It too will pass, but only if you work at establishing equal parenting roles and authorities.
The biomom should make efforts to include the nonbiomom as an equal authority in any and all aspects of baby care that don't involve the boob (yeah, even when postpartum hormones are raging!), even when society at large will sort of want to slot the nonbiomom in the "dad, and thus less involved" role. I especially think the biomom should take great effort not to employ boobs as a soothing mechanism for situations not involving hunger, very especially after the first itsy bitsy newborn blob stage, because if the boob features prominently as a comfort-giver and not just a method of food transfer, then the nonlactating parent can be out of luck in terms of soothing the baby because they just don't have the apparatus.
There is a lot of unspoken bias where the outside world tends to acknowledge the biomom as more the "real" mom, and you as a unit need to just lean gently against that. Have the nonbiomom hold the kid in the holiday photo and answer questions of random strangers about the baby, for example.
We might get more of the "oh, yours/hers" because DS#1 looks a lot like my wife, and DS#2 looks a lot like me, to the point that random strangers wonder out loud how DS#1 is really my son when I am out with him alone. It was important to us to use the same KD for both kids, so we didn't do the "pick donor to closely resemble nonbiomom" thing at all.
Anyway, having experienced both, I really and truly don't think there's any iota difference between my biomom and nonbiomom connection to my two sons, and neither does the wife... but we definitely had to fight for that at times when the baby was like, "uh, no thank you, nonbiomom, if you hold me I will scream my fool head off". Yeah, they both went through this uncharming phase, and emerged on the other side being equally bonded to both of their parents. That is definitely outsider-y feeling-inducing, and it is horrible and awful and it helps if you can laugh about how your baby is being the biggest stinker in the world and they just don't get to chose which parent is going to be taking care of them.