I had DS1 in December 2019, so he was 3 months old at the start of the first lockdown.
At the time I dealt with it by (almost manically) trying to see the advantages of having a lockdown mat leave. My DH was furloughed so that meant our baby got a lot of uninterrupted attention from both his parents, and I do believe that for a baby under 12 months or so that's much more important than seeing other babies. I breastfed exclusively until 6 months, because there wasn't much else to do. We got into a nice routine of taking DS1 for lovely woodland walks in the sling every day in the early morning when it was quiet and generally he had a very nice, gentle first year.
I felt grateful to have something to focus on during 2020, and a way of convincing myself that lockdown could be a positive (because of these benefits to DS1). And now at 2 and a half he is a sociable little chap and settled into nursery really easily this year - even if one of his first words was "Mask". I think if we went into lockdown now it would be much harder on him than it was as a baby as socialising is becoming important to him, and the playgrounds being taped off would make him howl now.
I do remember crying in the shower though, because I was so tired and worried and the baby groups I had been looking forward to were cancelled.
I now have DS2 who is the same age now as DS1 was when the first lockdown was announced. I have to say that mat leave has been a joy so far. It's great to be able to take the baby out to meet people and to just sit in a cafe with a coffee with him in the pram, especially after a rough night.
We're in the throes of 4 month sleep regression now but I'm so much less stressed about it this time, I think because normal life is carrying on and it's easier to keep a sense of perspective. I'm still breastfeeding but have introduced a bottle of formula a day to give myself a break and I feel really relaxed and positive about that, whereas with DS1 I got a bit obsessive.
So overall - I don't think lockdown was necessarily bad for babies. But it was fucking hard work for their parents.