New Circuit for 1.5HP Pool Motor

1.5HP at 120V is going to be around 20A Full Load Current, you CANNOT run that on a typical "extension cord", nor can you run it on 14ga wire and a 15A circuit breaker. The Code requires that the conductors must be rated for 125% of the motor FLC (taken from a table in the NEC, which is where the 20A comes from), so that means 24A MINIMUM rating of the wire. 12ga is only rated for 20A, so a 1.5HP motor will require 10ga wire and that means a 30A circuit MINIMUM (might be higher depending on the distance and voltage drop issues). So no matter what you decide (conduit in the ground or a temporary cord), it will not be a standard circuit/receptacle.

If your pump motor is reconfigurable to run on 240V, that would make the motor FLC 11A, so it might work on 14ga wire (again, depending on distance and voltage drop), but it would be 2 hot conductors, coming from a 2 pole circuit breaker.

Salesmen don't like to tell you the truth on these sorts of things because it might make you reconsider doing it, so they just say "Most people..." Gets them off the hook for lying.

Right off the bat, finish with your original intent, and hook the cable up to a GFCI receptacle that is inside the garage. Now come off the receptacle's LOAD terminals to your underground line to the pool area.

What you don't want to do is bring unprotected 120VAC out to a pool area and then fit a GFCI recep there. Because then, the wiring does not have GFCI protection, and the wiring can electrify the ground. Especially if NM cable is used, which is not made for outdoor use.

Anyway, continue off the GFCI's load terminals via UF-B cable buried with 12" of cover because it's GFCI protected... or run a conduit type of your choice from that indoor recep outside, then switch to 1/2" Rigid conduit for the underground run to the pool, this can be buried at 6" of cover (but it's expensive). Use THHN individual wires inside the Rigid conduit, do not put UF-B cable in conduit (won't fit anyway).

Use 12 AWG wire or cable.

As far as extending off the 15A circuit, yeah, you kind of painted yourself into a corner on that. I'd go ahead and replace that #14 run with #12 (or just run it alongside) and call it a life-lesson learned.

Violating the installation instructions is a bad idea. If anyone gets hurt at your pool (and electrical drownings are absolutely horrible, gut-wrenching, life-changing things), they will go over your setup with a fine-tooth comb. Any violations, you'll have a problem.