This is my 2nd baby and that’s pretty normal. Both my babies were like that too.
Dealing with the same with my almost 3 week old. Except he sleeps during the day and not long at night. This started from day one. He likes to lay on my chest. Im assuming the sound of my heartbeat is soothing to him. I would try white noise or heart beat sounds from YouTube.
I have no advice; my one month old is the same. I put him down in the day and he immediately wakes up and cries until I pick him up. I can’t get anything done but I’ve heard it’s normal for them to want to be held a lot at this age.