Bypass Mode connects the In jack directly to the Out jack through the 3PDT Foot Switch bypassing the circuit and should work even if the Main circuit is not working. That also means that since there is an issue with Bypass Mode this could be the entire problem. Recheck all wiring and solder joints between In Jack, 3PDT and Out Jack since that is what Bypass Mode is.
The solder joints on your jacks do look dry I’d first of all re-flow all of those making sure it melts nicely heating the wires and jack lugs at the same time to get a good flow and connection
Also check continuity on the 3PDT switch in both positions in one position the middle row should connect to the top row clicked into the other position (throw) the middle should connect to the bottom so in this picture one position 1 and 2, 4 and 5 and 7 and 8 should have continuity (effects mode) click the switch and 2 and 3, 5 and 6 and 8 and 9 should have continuity (Bypass mode) checking this will let you know if your switch is damaged internally from heat etc
This may not give you effect but we’ll at least hopefully get bypass letting us know the 3PDT is working and the jacks have a good connection