It can take a little while, but eventually you end up finding what works. My youngest is 15 months and if I could go back I'd probably start working on him sleeping independently from as early as possible, rather than my daughter. He still needs a lot of support to go to sleep now, and I think it's because I feed or cuddled to sleep because a lot of the time (which is my preference, but it's so hard having to support two kids to sleep 🫠), I usually had both kids on my own and I couldn't put both to sleep separately though
I went through this my my daughter and baby. My daughter was 18 months when I had her and had always needed a lot of support with sleep. She'll be 3 in a few months and at the very least needs me in the room with her for sleep, or if she's had a hard day and is a bit dysregulated needs me to be touching her. I know how hard it is to manage toddler sleep with a newborn! I ended up feeding my newborn to sleep while my daughter snuggled up to me on the bed to get them both to sleep. My daughter still has a lot of separation anxiety, so I can't say hey up with activities while I put the baby to sleep. I found getting my youngest used to sleeping on the go massage things easier, he now sleeps in the pram while she plays, or in the car on the way to activities. I've also started just not giving my daughter a daytime nap a lot of the time, she copes well without it, goes to bed really early and then I can put the youngest down a lot easier cos she's not making noise.