@Jones3A Such a lovely, considered response and what a lovely set of parents you are!
I agree that it's good to try to get to the bottom of the anxiety (if possible) - as you've been trying - but it does seem as if your DS might benefit from some counselling to help him build up coping mechanisms and resilience.
I was interested to read that most responders on here suggested letting him come and stay sleeping in your room but noticed in your response, that others later on suggested you set up a bed or sleep in his bed instead.
It is absolutely the latter I would go for. He clearly feels the need to be close to you, so that it is important, but by letting him go to your room, it's almost sending the message that his room is not 'safe' and you are 'saving' him by letting him stay in your bedroom (even if unconsciously).
When our DC were babies and toddlers, we always walked them back and stayed with them in their rooms (usually slept in their bed or stayed in an arm chair for a while) and then retreated when they were settled.
I do think like with babies, it is quite a good habit to make sure that they can self soothe in the sense that once settled, you may try to leave (i.e. so that he falls asleep knowing that you are not there anymore rather than him suddenly waking up wondering where you have gone - hope that makes sense).
Best of luck with it all. Your son sounds lovely and he's very lucky to have supportive and loving parents like you both.