My DM is like that - every little thing that other people just deal with and move on from is a huge issue she can't move on from and feels the need to recount it repeatedly to everyone she speaks to until the next one occurs.
She feels that her life is far more stressful than other people's and she can't understand why other people don't have the same difficulties as her with life. She is a very anxious person (always has been) and has accepted in recent years that she's probably got some sort of neurodivergence going on since we've been talking about it more as the younger generations of the family have been diagnosed and supported.
When I was younger, I didn't recognise it as anxiety and grew up calling it what she called it: "the [our surname] effect". Whereas now I know those same issues as anxiety, and not bad luck falling on us that simply doesn't affect other families in the same way.
I have found CBT to be quite helpful for myself with things like catastrophising and overwhelm, and I found learning to recognise unhelpful thought patterns really useful. Some people don't get on with CBT but there are plenty of other styles of therapy/support that can address similar issues,
With my DM, I can just take a break from her when she's getting too much and stressing me out, but with my SEN DC, I have to stick around and support them through it, so dealing with my DC's anxiety is perhaps slightly more similar to the situation with your DH, where you're stuck in the situation in a carer-type role.
Your situation is in the middle of these two situations, though - your DH is an adult who you didn't bring into existence so you don't have to take on the burden of his anxiety as your problem, you don't have to monitor his stress levels and anticipate when things might be getting too much for him or offer to help him and you can choose to just leave him to it and avoid the stress by leaving the room and giving yourself some distance from it. Which is perfectly reasonable for you to do, despite the fact he might prefer you to stay and talk him down. You're not obliged to be his carer and if you do decide to take on that role in his anxiety management, it's absolutely your choice (although I know first-hand that it's easy to fall into that role in a relationship without even realising!).
I would probably talk to him about it, explain how it's affecting you and ask that he seeks some help. And mutually agree a strategy whereby when he gets like that, you will be walking away to manage your own stress levels, so he understands that you're not abandoning him but managing your own MH for the benefit of the household.
Hopefully he will seek out some help (therapy, medication, whatever works for him) and things will start to get easier. And don't underestimate the benefits of basic things like sleep, exercise and healthy diet for anxiety management too - the simple things can sometimes make a huge difference!