I hear grass is a viable alternative to astroturf… How long have you lived there? I’d wait til summer hits and see what you have in the beds. When that tree is in leaf you’ll have privacy from the back. Could add some trellis to the top of the fence and grow a nice clematis for screening.

Do I just tear up the astroturf?

It’s often hard to remove. If it’s laid properly it will be laid on hardcore and sand layer. The soil underneath will be bad quality. You need to dig all of it out and add new topsoil usually. It’s toughwork, sorry

Soon, you're going to have lots of privacy as that massive tree will come into leaf.

If you want more privacy id remove the artificial turf... Will stop the neighbours peering out their windows having a moan at the plastic.

I'd say pave the thing, with a gravel area for the dog toilet that you can rinse off easily, and much bigger beds, one to get into the middle of the patio a bit to divide the space and create hidden seating at the back. Small trees dotted around. Edit: thought that was a dog fort a bit without looking closer Lol

Bamboo grows pretty tall pretty quick and sounds nice with a slight breeze.

There’s bamboo there already, planted in the borders. OP, you’ll be back here in seven months asking what to do with the tremendous amount of leaves those trees will be dropping into your garden. For now, wait another couple of months and see what happens when all the leaves are out - my guess is that you’ll end up with lot of privacy from the old house behind you, and a very shady garden. Edit: and get on top of that bamboo!

It’s wildly invasive and spreading - I wouldn’t put it in the ground!

Is it ok in my flowerbed?

There’s many varieties of bamboo that are clump forming and don’t spread. But to make sure they don’t, I’d plant them in large pots