This situation - one partner works, the other is sahp, then as the kids age the working partner has high income and the sahp has much less to do but has become unemployable except for crap jobs or looooong and expensive retraining - is quite common.
Recognise that if he is doing more housework and family admin than you, your DP is already making a financial contribution. If he was just lying around while you paid for a chef, cleaner, laundrette, and driver, that’d be different, but it doesn’t sound like he is.
Recognise also that your career was in part built on his contribution at home. If you’d been doing your 50% of the childcare, cooking, and housework, throughout all the toddler night wakings and school holidays, you would never have achieved the income you have now: your contributions and performance st work would have been much lower. It is family income, achieved by both of you. It is not just yours. You are taking all the credit for your current income but that isn’t fair.
His self-esteem will be very low, he may even be depressed, and this does not lend itself to enthusiastic job-hunting.
Remember also that you should have both discussed this more clearly when he became a sahp.
I suggest the first step is marriage counselling to help you recognise the contribution he is making now, and to focus his mind on what he wants from the future.
I do think it’s sad that your income is now so high that it can afford to support all of you, but you want him to take menial jobs like cleaning. I don’t believe that if he got a job you would suddenly start doing 50% of all the housework, and I don’t think him being a cleaner or whatever would cause you to respect him more.
The real problem here - and again its very common - is that you’ve grown apart. You travel around meeting people and feeling important and mixing with high-earning men while you DH stays at home doing the same old drudgery, and you simply don’t have much in common. Work on that. Do some of the drudgery and let your DP find a passion of his own, which may or may not be paid, and you’ll have more in common.
But to expect a sahp in his mid fifties to take on menial jobs when the family doesn’t need the money, in order to earn your respect, is not cool. Mid fifties is not an unusual retirement age and was standard for my parents generation, some pensions still start at 55.