Low volume and terrible audio quality from Headset with 3.5 Headphone Jack, speakers and Bluetooth work fine

From your description you may need an adaptor for the headset jack like this:

Sound only if headphones are half plugged in, work fine in windows

The wiring standard can be be tested by measuring resistance across jack connections
Headphone connections would be 16 Ω or higher
Microphone would be 1,000 Ω or higher
3.5 mm Headset: Accessory Specification  |  Android Open Source Project

Headphones with a 3-pole TRS jack plug would not be affected