Skin to skin contact
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Have you tried baby wearing so you can at least have your hands free and move around while he can get that contact? It’s does take practice to get them to get used to their bed again but he’s so small still he may just want that contact for now. But in time it does get better but right now will be really tough. I recommend baby wearing to help meanwhile.
I also did skin to skin and contact naps pretty much all day/for every nap and it 100% does get better/easier. Your baby is just so used to your smell, heartbeat, movements, warmth, voice, etc, that when they are suddenly away from it it is different and strange and that's scary. If youre able to, just give all the snuggles you can and when baby is awake, thats when you can step away got a second (not like another room obv, just like not physically touching) to kinda get him used to it slowly while awake so it isn't scary and strange when he sleeps.
It will settle. You have to remember your little bub spent 9 months in you and knows your warmth and heartbeat. It's comfort and safety for them. My health visitor said at this stage contact naps are so common and they won't associate cots etc until after the newborn phase of 2 months/3 months. I would soak it uo while you can get the cuddles in but I also know that it is tiring and relentless trying to put them down when you need to sleep too! Me and my husband take turns when she wants contact naps.