You might find this an interesting read
https://www.happiestbaby.com/blogs/baby/contact-naps

It’s not an issue unless it’s an issue for you. But I would start minimizing the touch, so start with bubs down and hand or back patting them no hands and just a shhhh then slowly go down from there

I had this with both my children and to be honest I just did what felt natural. We bought cots for both of them and never used them. I did notice that once I stopped breastfeeding, it was easier to transition to napping on their own but sleeping at night on their own took a few years. Everyone is different and you have to try and do what feels right for you and your baby. My doctor always said unless it is impacting either of you negatively, there is no reason to stop.

What’s the rush?

For thousands of years children slept next to their parents. Now in mainly western countries, we can’t wait to kick the poor toddler out before they can barely walk. For what? A toddler doesn’t need to be “taught a lesson” on independence (what’s next, “get a job?”), they need to feel safe and secure at night.

Of course they’ll grow out of it. Having them in the same bed can be inconvenient, but nothing that can’t ultimately be worked around. IMO, enjoy it while it lasts.

Are you able to wait until bubs falls asleep and then move them? Maybe keep them nearby. A clock or other beating/clicking noise may help them feel at ease during this transition.

I’d put my jumper in the bed so he thinks I’m still close, works wonders

its been awhile but our son never wanted to sleep in his bed ,cot or day napping without being close many a times fell asleep myself with him in our arms ,till i was that buggered i put him on his bouncer gave him his bottle didn’t burp cause he was already comfortable , first few times when he finished his bottle (water with a bit of grip water or hint of honey)he complained but the third time he fell asleep on bouncer so that became routine afternoon nap i was breast feeding . hope this helps

Try just gradually reduce the amount of contact time, and make sure their environment is conducive to sleep. Overall, the best would be to create a bedtime routine and stick to it, being patient and consistent (also avoid letting your baby nap too long during the day).
If your baby wakes up during the night, try to soothe them back to sleep without picking them up.

How old is your son ? and do you breastfeed ?
My first thought is try to involve your husband/partner in the overnight routine, so he doesn’t grow totally dependent on you.
Otherwise you could also place an item between you and your son (like a small pillow) and rather than full body contact just hold a hand

Have you tried sleeping with his sheet for his bassinet the night before so it smells like you?

I’d read up on swaddling. It worked wonders for me.