Oh god, I found a toddler and a newborn so hard. And felt shit about it because everyone on here seemed to be saying that being pregnant and having a toddler was harder than toddler + newborn. DD was 2.5 when DS came along and we moved house when baby was 2 weeks old. Total madness and probably the hardest time in my life.
I felt completely unable to focus on toddler if the baby needed me. None of that 'read books with your toddler while you bf baby' stuff worked as DS was a wriggly feeder and DD used to just interfere with him (patting him, stroking him, sticking fingers in his ears - all in a loving way, but distracting nonetheless). I found getting out the house with both of them almost impossible as the baby would always need a feed/nap/change at awkward times and DD was/is not very independent, so would need a lot of attention and interaction from me if, for e.g., we were at a toddler group.
And we found it this hard even though DH works from home, so was around a lot. How we coped was getting more childcare hours for DD, essentially. And just accepting that for a while DH would be DD's primary carer at home (e.g. getting her up in morning/ doing bedtimes) while I looked after the baby.
Anyway, slowly slowly it got easier and now that DS is in a decent routine and taking long naps without much assistance (he's 7 mo now) it's a bazillion times easier. I'm able to leave the baby for periods of time to go off and do things with DD, so we're 'reconnecting' and the baby is better able to come 'along for the ride' when we're doing things with/for DD. And the wonderful upside is that DS and DD fricking adore each other in a major way. He's the first thing she asks about when she wakes up every morning and he lights up whenever she's around.
So no, I don't think anyone's been permanently scarred by the first few rough months. Hang in there. It will get easier. I promise.