Electrician here, you should take everyone’s advice and contact a licensed Electrician to trace out the wires and see exactly what is what.

Now that that’s been said, were I to come and look at this issue, my first check would be to ensure that the little tabs on the outlet are still there. (Little red squares in photo) You could be getting an opened neutral if that tab is busted. The blue power wire looks to just carry onto the next outlet or device. Meaning that this outlet will only work when the switch is on.

Whenever we install a switched outlet we would leave the bottom outlet with constant power, and only switch the top half of it. This is when you would remove the little tab on the HOT side, to separate it. The neutral tab should still be intact.

Next would be to check that the wires are all Connected well under the marrettes or wire nuts. Wires will sometimes break or snap at the marrette through over tightening.

I drew up a quick wire diagram of what we know from the photos.

If those tabs are gone for whatever reason, I would replace the outlet instead of trying to add more wires.

https://cdn.discordapp.com/attachments/718892278931783726/1080189524740681849/IMG_1393.jpg

Hope this helps a bit.