I should clarify when I was speaking of a controller I wasn't referring to a COG or driver, but a controller that would interface with the driver. Having a controller on the LCD would mean that it was a custom assembly and would make it even harder to find a replacement.
Looking at the FPC cable, U1 could be a controller yes, but that is more likely to be the touchscreen controller probably an FT6236ish type controller like this [https://www.buydisplay.com/3-5-inch-capacitive-touch-panel-wiith-controller-ft6236-for-320x480-dots]. I would assume there would the a LCD driver (such as He would have to trace the wires. It's not uncommon for companies to use older connectors such as the 50 LCD connector typical of an 6800-series parallel interface or
8080-series high speed parallel interface verse using the same connected and repurpose the lines for 3-lines serial peripheral interface and 4-lines serial peripheral LCD screen.
I have used for example
https://www.crystalfontz.com/ to get a replacement LCD working with some units where I didn't know what the actual OEM product was.
By comparing to say the interface table they supply you get a sense as to what the specs for this particular LCD might be.
https://www.crystalfontz.com/products/document/2236/CFAF320240F_Series_Interface_Table.pdfSo if were to map out the connector and give us a clear picture of U1 we might be able to narrow down the interface required and make it easier to source an equivalent replacement.