It needs an 8-pin PCIe cable from the power supply. If you can get at one and route it through to the new card then it will work. Note though, as Tony says, 450W may be cutting it fine and you could get system instability when playing demanding games.
The 5800x isn't that much faster than the 5600 and consumes more power so running 24/7 would cost more than the benefit. You have a limited system running AM4 on micro ATX so I think a new build is needed on AM5 with a more powerful CPU and faster memory. Running 24/7 you need to factor in...
You will be able to find the order if you log in to your account even if it's over 10 years ago. As long as you have the same email address you can simply change the password and log in.
For a basic 1080p system, your original build looks OK to me. The SSD will do for older games, as will a 4060. The saving on your OS allows for the better PSU in case you change your mind later on about upgrades. Other than that it's fine.
I wouldn't advise the 8GB 4060ti. In some games this card will run much faster with 16GB and this will only get worse with future game releases and patches.
Then you are wasting your money. A 7800X3D paired with a 3080 should be fine, so following your logic about memory requirements, then a simple upgrade to 32GB would solve your problem for <£100.
It isn't worth spending that much on such a low end system.
I would recommend:
iiyama G-Master GB2730HSU-B5 ~ £130 from various retailers.
It's a 1080p 75hz monitor which is more than adequate.