I had my first baby at 35 (very nearly 36), and second at age 40. Got pregnant pretty quickly each time, had overall quite easy pregnancies, and healthy births. My baby girl is now 6 months, and my oldest is 4.5 years old. I was worried about balancing work and parenting on no sleep, but honestly, everything has been great. It helps to have a super supportive partner, and have access to good healthcare. I also live in Spain, where older motherhood is the norm...so know that you are in good company!
We did all the screenings, to rule out chromosomal abnormalities (tbh, I think that we wouldn't have continued the pregnancy had the baby had a serious problem). I was also super worried about how the dynamics would change—both between me and my husband, and also me and my daughter!
It did take my daughter a bit of time to adjust, but now she adores her baby sister. It helped that we had my parents come and stay for a few months after the baby was born, and my older daughter continued to go to daycare. That gave me time to really spend one-on-one with the baby while my older daughter was away. And then I always made sure that someone else had the baby so when she got home, I could fuss over her and spend some one-on-one time together. Now she isn't worried about competing for attention, and it's quite happy.
Which is all to say—even though you know you'll love your baby, all the new responsibilities that comer with a new littler person is scary! (I was terrified!) But know that it can all work out beautifully, and probably will!