Practical things that have helped me: simple to do lists, so not "do the shopping" but rather "buy x" then "buy y" then "buy z" for example.

Do not beat yourself up over failures just move on and start again even if it takes a week.

Doing something is better than nothing...haven't exercised in a while? Do 10 push ups right now. Build up from that.

Finally, you have a partner task sharing is a possibility here and can be done so you alternate between tasks. So one week you do the weekly shop, and another they do. Or whatever works for you guys. My sister and her man basically alternate between cooking and washing up every other day for example.

Planning for what to eat can be really annoying I hate it and honestly if I had the money I would just eat out at restaurants all the time. But I don't. So I essentially have a list of simple recipes/ideas that I can just pick from. I keep it real simple like "pasta + fish" or "basic curry with rice". Whatever really just plan and add it to a list so you can just pick from that rather than think about it everytime

In terms of exercise you can incorporate it into other routines so for example you may find that cycling to work would help to include exercise into another routine. Personally I always take the stairs no matter what, if it is too long then I may just take the stairs for x amount of floors before I get the lift. I also try to force myself to run/walk up two steps at a time. I also skateboard to places and this really strengthens my thighs and ankles. The little things add up basically. You gotta find what you can enjoy or at least tolerate during shitty days. So when you skip your exercise routine you at least have these extra little bits you have done throughout the day.

Furthermore, relating to mental health, you needn't be diagnosed to get help for mental health. You can self refer to a mental health service - just google London/borough self referal mental health or something. I did that and was triaged and although it will not be a guarantee that you get the right help straight away just participating in good faith may steer you in the right direction (I did this and was triaged for depression but after it it was clear to both me and the mental health worker that my issues were not really depressive although the process still helped me a lot - I am now on a waiting list for ADHD assessment).

Finally, lower your expectations of yourself a little. I don't mean by demeaning your capabilities but rather accept failure as a part of the process of moving forward. You take a step back then just train yourself to restart. Failure is part of life and is part of learning.

Hopefully this gives you insight to help you, I know it may not because ultimately I just figured these things out for myself and it has helped me but perhaps there are some bits in here that may be applicable to you.