advice for toddler new bedroom

my family and i are moving into our own place that’s gonna have two bedrooms, so my son is going to finally have his own bedroom. however, he has always been in the room with me and his dad (1 bedroom apartment at first and then living with other people he didn’t have a chance to have his own space)

i’m writing in here to ask do you guys have any tips and tricks for him to fall asleep on his own/stay in his own room? he currently has a toddler bed that’s right next to ours but i can’t for the life of me get him to sleep on his own. i either have to lay on the floor next to him or lay with him in my bed and then transfer him once he’s asleep. i’ve tried the “lay him down while he’s awake” trick but he immediately gets up and follows me out of the room or if i have the door locked he’s just screaming and crying until i get him and there’s been times where he’s thrown up from crying so much & that’s not something i can handle.

it literally takes him HOURS to sleep even during naps and sometimes i just give up on a nap all together and then try (key word: try) an earlier bedtime and it’s the same cycle

his current “routine” (i say routine very loosely)

8-9AM - wake up, breakfast
10-11AM - outside time/independent activities, snack
12:30-1PM - lunch, attempt at a nap (if he does fall asleep he naps for about 1.5-2hrs)
2:30-4PM - wake up, a small amount of screen time while dinner is being made
6-7PM - bath time, quiet time with a story
8:30 - bedtime attempt, but he truthfully doesn’t fall asleep until 10:30 almost 11

does this seem like a reasonable schedule or does something need changes?

my husband and i do want to try for another baby soon and i want our toddler to be a good sleeper before that happens.

TL;DR: We’re moving into a 2-bedroom house and my toddler will finally have his own room after always sleeping in the same room as us. He currently cannot fall asleep without me laying next to him or transferring him after he falls asleep. If I leave while he’s awake, he follows me or cries/screams, sometimes to the point of vomiting.
Bedtime can take 2+ hours, and naps are a struggle too. We’re hoping to have another baby soon, so I’d love to get him sleeping independently beforehand.
His current schedule is roughly 8–9 AM wake-up, 12:30–1 PM nap attempt, and 8:30 PM bedtime attempt (but he usually doesn’t actually fall asleep until 10:30–11).
Any tips for getting a toddler to sleep independently, and does his schedule need adjusting?