Op hasn't mentioned what her ds is like with other people and at school/friends/other situations. I suspect that he is in fact far less anxious because others don't pander to it in the way op has. I also suspect that the op's dh isn't being mean at all but that after seven years he's fed up of this child's behaviour being enabled by the op to the extent that in her op she criticised her dh for not getting up from his computer to watch him.
I don't imagine this child became this anxious overnight, I suspect that the anxiety increased because at the first sign of it op said she would watch him, and so the cycle began to the point where he has a screaming tantrum if she won't watch/follow him. At seven, which he presumably doesn't have elsewhere or for other people.
there is a balance between reassuring a child that no, there isn't anything to be afraid of but equally not pandering to the anxiety to a point where the child is screaming.
I had some anxieties as a child e.g. not wanting to get up in the night or want to fall asleep on my own (I did though) but there's no way I would put up with a seven year old insisting he be watched/followed everywhere in the house and screaming if I didn't comply.
Op needs to take a more hard-line approach. No of course there isn't anything to be afraid of, yes, the only way you can know that is by going there and seeing for yourself, and when you get back from there you can tell me that nothing happened, and you will see that it's not scary.
But I would take a 0 tolerance approach to screaming. Reassure that there's nothing to be scared of while having a conversation, but have a screaming tantrum and I would leave the room and shut the door, with no option for him to follow
This child has learned over the past seven years that the house is scary, it has to be, because his mum watches and follows him wherever he goes to make sure he doesn't come to harm. She has reinforced that fear over time, and when she steps back from it, all he has to do is scream for her to come back and make sure he doesn't come to harm again.
The op needs to break this cycle. no more following him anywhere. no more watching him from the stairs, draw a map of the house which goes on the fridge, and on which he can plot his movement around it over the course of the day, with perhaps a marble or sticker or something for each room he's been to, but only if he's been there alone.
But the cycle needs to be broken for a number of weeks before immediately looking to seek a diagnosis. Most likely it's a reinforcement thing, not a sn thing. Lots of children have anxieties for all number of reasons, the more we pander to them, the more we reinforce them. And most don't have SN.