Hi OP. I'm pregnant with donor sperm for similar reasons to you - our baby's finally due in a few weeks after a 5 year slog with infertility - and we couldn't be more excited.
The main thing I will say is that you are absolutely NOT "having another man's baby".
A sperm donor is not a dad and you are not having his baby. You are using some of his biological material because of a medial issue - that's all - in a similar way as a blood or organ donation. You are having yours and DH's baby - you have just had to take another path to get there.
Your DH will be this baby's father in every way that matters - although not biologically linked, he will still be the reason that the baby exists (you wouldn't have had this baby without him). He's the only father the baby has, and the baby is going to need him and love him in that role. He will influence and shape the child's life the same as any father.
I do find this a reassuring way to think about it - DH still had an essential role in bringing the baby into the world and the baby's existence wouldn't be possible without him.
Emotionally, myself and DH are both feeling incredibly connected to the little one whilst we are preparing for the arrival. DH talks to my bump, is doing all the other parent preparation, NCT group etc, and he is very excited to meet the baby as any father would be. Once you are pregnant you will be surprised how you just go with the motions as any other parents do.
Obviously, both of us have been dealing with all the feelings about not being able to have a child that was genetically linked to him. It would be a lie to say that's not a thing at all, of course it is - however, there's a process of grieving/ letting go, and loving and celebrating the child that you can have.
It doesn't impact how he feels about being this baby's father.
I'd echo the above poster's advice about joining Donor Conception Network. We've been to a few helpful events and online talks with other people in similar situations. My DH found it especially helpful going to a men's only zoom talk about sperm donor conception.
Good luck with it all OP - and if you do go down this route, it will be OK.