2019 Base model MBP is dead, need advice. Logic board failed after updating to Ventura from Monterey

I would cut your losses like you were thinking. The Logic Boards for the MBPro 16" (2019) model seem to have a much higher rate of failure than any other model. Plus, the laptop is three years old....in another year or two you will likely need to replace the battery (official Apple battery replacement is $250 US or possibly more depending how the AASP handles the replacement).

Apple will only install the exact same model of Logic Board.

Unofficial repairs are tricky with the 2018+ Macs. The various parts are paired together....it is hard to say exactly what this means since Apple doesn't explain anything. The only parts that I know for sure which are paired are the TouchID button and the Logic Board. If you don't have a properly paired Logic Board & TouchID, then you will not have fingerprint recognition (it will still act as a simple on/off power button). Even Apple is unable to re-pair a used TouchID to another Logic Board since Apple forces AASPs to replace the TouchID whenever the Logic Board is replaced (adds almost another $100 to an already expensive repair). I know that Apple uses a proprietary service utility to configure the replacement parts to the system....I don't know what happens if this is not done, but there is a chance macOS may see security as decreased for certain features (HD video, Apple Wallet, etc.)...or it may not affect it....hard to say. I have seen a simple innocuous macOS setting cause macOS to report system security was reduced and would not allow the use of a certain feature....it was a setting that I would never have guessed would cause macOS to complain (it was not any advanced or hidden setting either).

I think investing the repair money into a brand new laptop is the more economical option.

Hi,

If I were you, I would MacBook Pro to Trade-in and get new Apple silicon MacBook Pro.