That sounds difficult OP, and I understand something of your position possibly.
As a lone parent to 4 DC, you are possibly so accustomed to getting on with things, making the best of things - it's like a treadmill, and you don't have much space to reflect or analyse what this man is bringing to your life.
I do understand the MH concern; I am very similar. But this is not a reason in itself to remain. In fact, it indicates you have work to possibly do on yourself. The relationship has become familiar, comfortable and even a habit. Like a comfort blanket. The person you check in with day to day, and it's very, very hard to walk away from that when you are a lone parent. But you owe it to yourself to analyse and examine your feelings more. Are you coming at it from a place of need or a place of want; has he become a familiar and comfortable habit? How can you build resilience to your MH so it is less fragile and likely to be greatly diminished in the event of a breakup?
I have been in a very similar spot to you. Recently and painfully broke up with a 3 year relationship; like yours, also didn't live together and I am a lone parent to 3DC.
It has been very very hard. But when I examine my feelings very closely, they are not necessarily all deeply related to him. They relate to all sorts of things, bruised ego, loss of comforting routine, fear of the unknown, feelings of rejection and shame stemming from inner child, other/deeper trauma that was activated by the split. The split is in a sense a placeholder. Yes, it hurts. But like you, I had a growing number of niggles and doubts. My rational mind is far far further along than my bruised heart.
But the work has to be done, and a relationship that is a crutch of familiarity will never truly enable you to grow. I did free counselling on the NHS ahead of the split, and am now trying to work hard on myself after. But I know the pain is not just about the break up, but about surface ego pain and also deeper older trauma, and THAT is where the work needs to be done.
So my advice would be unpack your feelings a bit. The relationship cant be a crutch for your MH. My MH is very fragile also, so I do understand. I was on sleeping pills post-split. But that sort term pain is not a reason to move on with your life.
If I may also say, as a single parent of 3DC, this leaves us extremely vulnerable to making an 'inner compromise' within the transaction that most relationships depart from. You overlook various things/take a hit on things, simply because it is nice to have the outlet of a relationship. I am focussing on making myself so strong, so resilient, that I won't need the crutch, and that I won't make any internal bargain with my standards. Good luck OP, look after yourself.