Working on a puppy schedule, would love and appreciate input!

Hi all, my partner and I recently adopted a puppy a few days ago and now we’re trying to figure out a proper schedule for him. This is what I have tentatively planned, but any and all advice/constructive criticism is appreciated! He’s 3-5 months old (surrender papers and adoption papers are listing different birthdays: his surrender papers have him at 5 months and his adoption papers from the shelter we got him at has him at 3 months) and we think he’s some sort of terrier mixed with chihuahua. Of course this isn’t something set in stone, and variations are going to happen but in general, we’d like to keep it around similar guidelines.

-7:15/7:30am – wake up, bathroom walk only

-8:00am – breakfast, play (tug of war, fetch to spend energy)

-9:00am-10:00 – longer walk (bathroom, explore/get used to city sights, sounds and smells) or if weather is bad, just enough time to relieve himself and then play indoors*

-10:00am-12:00 – naptime/quiet time in crate

-12:00pm – bathroom walk after waking up, lunch (frozen kong with a kibble-wet food-water mixture if he’s able to engage with it?), play

-1:30pm-2:30 – longer walk (or bathroom walk/indoor play if weather is bad*)

-2:30pm-4:30 – naptime/quiet time in crate

-4:30 – bathroom walk, play (training session?)

-6:00pm – dinner and then hang out in crate with maybe a treat while we get dinner/eat

-7:00pm – out of crate and playtime

-7:45/8:00pm – last walk of the night (put away living room floor bed+blanket/most toys before leaving so he’s encouraged to seek warmth and coziness in his crate and not in the living room)

-8:30pm/9:00 – wind down and bedtime (no engagement except for pets and redirecting to a chewing toy if teething is especially bothersome)

*check on him around 10/11 and see if he’s up (bathroom walk if so but if laying down/lazy, let sleep through the night)

He usually knows to go into his crate after a walk although I’m not sure if he’s fully napping in there or not. We cover the sides of the crate with a blanket since we do that before bedtime as well to hopefully associate the blanket covering as time to sleep. He’s certainly curling up and laying down so he seems to be relaxing in there at the very least, but will react at times to noises/will track us when we walk around, and sometimes will be sitting up in front of the crate door just an hour later. I’m concerned that he’s not getting as much total sleep as a growing puppy should.

Thank you all for your help!