I think there is something really unpleasantly slippery about this message, because although it reads as apologetic and reasonable, he is setting out his version of what happened as established fact while continuing to withhold the information that would allow you to establish that for yourself. He tells you there were no “wild spends” and that it was simply things building up over time, but given that he successfully hid the debt from you, I’m not sure why you should now be expected to accept his reassurance about what the statements contain while he refuses to let you see them.
“I’m managing that mistake” is doing quite a lot of work too, because he has decided what the problem is and therefore what resolving it looks like. In his account, the problem is the debt, he has a plan to pay it off, and looking through the statements will not “solve anything”. Yet the much bigger problem now seems to be that you have discovered he is capable of seriously deceiving you, so you understandably no longer know whether what he tells you is true. Seeing the statements might help you establish whether his explanation stacks up, whether you now know everything and whether there is any basis for rebuilding trust.
He's positioning your need for that as unreasonable, even coming up with shite like "I can't go back in time", like you literally asked him to time travel and I'm just being oh so reasonable and, I mean, I can't time travel".
I find the ending particularly disturbing, especially given what you have said about him becoming angry and storming out when you challenged him. “Wherever you stand, I’ll respect” sounds very reasonable, sure , but then he moves to understanding if you don’t want to be with him and finally to “there’s no point in living with resentment or living being resented”. I find it very difficult not to hear an implicit threat in that, because that's how he wants you to feel.
He has done something which has given you extremely good reason to resent and mistrust him, yet he is already introducing the possibility that the relationship cannot continue if you remain resentful. He knows you feel stuck there with small children, and he's outright threatening your safety and security by blackmailing you to shut up. "If you stay like a naggy old shrew about all this, I'm going to make you scared I'll leave you" would have been a more honest read of that part.
There is an entirely legitimate position in which you choose to stay while remaining angry, asking difficult questions, requiring complete transparency and taking however long you need to decide whether he can be trusted again. His message leaves bugger all room for that. He has a plan, he cannot change the past, looking at the statements supposedly achieves nothing, and if you remain resentful then the relationship is over.
For me, the debt is almost secondary now. The bigger issue is what he has shown you about his trustworthiness and what he does when that trustworthiness is questioned. He concealed the debt, became angry when challenged, still refuses to provide the information that would allow you to verify what he is saying, and is now beginning to position your reaction to his dishonesty as a potential problem for the relationship. He seems to want you to trust him again while denying you the means of deciding for yourself whether that trust is warranted, and at the same time is already setting limits around how he expects you to feel about what he has done.
This was a shitty thing to do, and it's not about the debt. It's about how he'll lie, turn any legitimate feelings you have into an implicit threat to leave you, and make your feelings the problem. I wouldn't stay for this one. You only get one life. I've watched a colleague live through this and it broke her over time.