Basement – Installing Basement bathroom exhaust fan in a side wall rather than a ceiling

I'd recommend venting out the gable. Run a rigid vent from the gable wall to a point near your install, and use a 2' piece of flex duct to connect the fan to the rigid vent. The flex duct makes the bends easy (don't kink it) and allows the fan to be repaired from below in the future. For that length, I don't think you need to worry.

You have two big issues here.

First is that you have a serious risk of venting sewer gasses into your home. This is why drain vents open above the roof line or use one-way air admittance valves. This is likely to be unpleasant and possibly unhealthy.

Second is that a drain vent is typically too small and too moist to properly vent a bathroom fan. Your fan is probably designed to use a 4" duct, and instead it's going through a 1.5" diameter pipe. And if any lint/dust gets pushed out by your fan, it risks accumulating on the sides of the vent pipe, potentially blocking the pipe and slowing both your drainage and ventilation.

Beyond those functional problems, you'll also have a pretty visible issue that anyone inspecting your attic will see. You should do this the right way: add a properly-sized duct line and a roof vent for ventilation, and re-seal your drain vent pipe.