I am sorry to hear about your loss, my condolences. In terms of loss of motivation, however, there is nothing like getting outside with only the sky above your head, it is indoors under ceilings I have had all my worst moments.
That is very different from your first picture, the regenerative powers of nature are amazing, and I expect the cat enjoys it like that, however your neighbours may not be so pleased when it all goes to seed and starts spreading into their garden. It will be doing the soil some good, it looked rather trodden and compacted before, and put through a mower and shredded a bit it will make a good basis for a compost heap. Taken down with a hook is harder work and it will take longer to compost, but either will work. Best done before it becomes full of seeds.
I don't know how much rain you have had, down here in Sussex it is bone dry and digging has become a job for a pickaxe, so you might want to leave that until it is a bit damper, but get out there. There is nothing like 'outside' to help one's mental attitude, and it almost doesn't matter what you do, when it is like that it will show, there will be some achievement.
Sometimes it can look overwhelming, but a flower bed is created one spade width at a time, little and often is the way forward, don't exhaust yourself. I am coming up 78 this year and in the last couple of years I have put a large garden into order and created new flower beds and veggie beds. I am out there for a bit almost every day. Nothing happened quickly, but there is a cumulative effect if you keep doing it. If you go mad, work yourself into the ground and flatten everything at once, I can almost guarantee you will be right back where you are this time next year.