Not sure exactly where to put this, since there's no "xperia" category in the devices forum. Anyway, here goes:
For the past month or so, the USB port on my Xperia X has stopped "locking" a cable in - you plug it in and the cable just slides out, like an ethernet cord that's missing the little clip. I've been making do by standing the phone up vertically and relying on gravity to hold it onto the cable.
Recently, it's gotten more and more finicky about actually charging. I have to wiggle the cable and get the exact right angle. As of yesterday I can no longer get it to charge at all. Given that unlike the N900 the battery is not removable, is there any way to fix this USB port issue so I can continue to use the phone?

Possibly, start by looking at here

https://www.ifixit.com/Device/Sony_Xperia_X

Competitors?

https://www.ebay.co.uk/itm/New-Repla...0AAOSw89pborGe

or cheaper from Aliexpress

https://www.aliexpress.com/item/Orig...a-018170bc8562

It is very easy to replace

Have you considered cleaning it with a toothpick?
I had the same until my friend cleaned all the dust in there.

True, the biggest issue is a) to open the back panel which is made of aluminum and dents easily, b) shield the panel when you put it back.

You have to heat it a little. It is doable with an hair dryer. To glue it back there are stickers on ebay for less than 1€

I did send my device (X) for repair under official guarantee, it came back fixed, but the back panel at some corners came loose. I've ordered 3M stickers from ebay and tried to repair it few times unsuccessfully.

Actually some time after the repair the device stopped charging. I thought the USB socket was damaged and ordered a new charging port, just to find out the port connector to the mainboard was not plugged in properly (not really impressed by the official service).

As the back panel is made of aluminum, it gets slightly distorted/twisted when it gets removed. The twist is very slight and almost impossible to make it straight. Then when you put it back after some time the pressure of the twisted corner comes slightly detached . At least, that's my experience.

I was considering buying a brand new back panel, but I could not find a complete one, i.e. back panel plus camera glass, plus some copper stickers (which form part of the main device circuitry?)

Still available:https://www.replacebase.co.uk/sony-x...lens-grey-oem/