My now 10yo was the worst sleeper for so long! First 2 years were sometimes every 45 min wake ups at time and generally every 2 hour wake ups. Then she would wake for the day at 4am. We used to put her to bed at 6.30pm as that was the best chance of getting her to sleep as she never woke any later if we put her to bed any later - just woke up tired and grumpy. From about 4pm onwards she was bouncing off the walls and if we did ever keep her up late she was completely dysregulated and screaming.
Naps often took 45 mins of rocking to sleep get a 20 - 30 min nap.
In short she was a bloody nightmare.
Somehow we thought it was a good idea to have a second child, who luckily turned out to be very different. Not a good sleeper, but far easier than her sister. She still woke lots, but you could keep her up later and she would just eventually fall asleep, as she got tireder. She woke at 4am too but didn't bounce off the walls, she would play quietly. Crucially, she loved naps & napped for 3 hours a consistently in her cot. It was an absolute game changer!!
My survival strategy for baby 1:
Sleep when the baby sleeps - if they will nap for 30 mins, take it.
Lower your expectations of a tidy house etc - survival and your sanity is key.
Take any offers of help you can get eg taking them to the park for an hour - use that hour to sleep.
Loads of exercise ( preferrrably outdoors) and cognitive stimulation - the only time would did get longer toddler naps was after big hikes or bike rides. Making her brain work had the same effect - doing jigsaws, colouring, reading etc.
Drop the naps and get out. We just excepted rather than spending 45 mins rocking a toddler to sleep for a nap to let her crash out in a sling/ car seat or buggy if she was going to nap.
As she got older quiet activities - colouring/ lego/ reading/ stickers/ audiobooks at bed time. She can stay up late but she must stay in her room and be quiet.
Now 10yo prob goes to sleep 10.30 until 7.30 and that works for her and us. I do think she has ADHD and needs lots of help with regulation still. It's very obvious looking back, she looks insane in every toddler/ preschool video we have, with her baby sitting sitting calmly next to her.
Remember every child is different - what works for one child and family may not for another and that's ok.