The jack is electrically in the path between the processors and the speakers (internal and external).

Your options:

Try gently cleaning the jack with a plastic pipe cleaner and a small amount of Isopropyl Alcohol 90% or electrical contact cleaner.

Replace phone

Replace jack

Get the jack pinout and bypass the jack on the motherboard

T_O

PS FYI, Information on Tip Ring Sleeve Jacks
TRS connector - Wikipedia, the free encyclopedia

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The_Omni