I’m pretty well using the stereo version of that with my pigtail
The audio jack on the Pi doesn’t work the way it does on a PC. As far as I know its not going to auto detect that you plugged something in and toggle from HDMI to analog automatically. And even if it did, by soldering your amp onto the test pads your hooking things up in parallel. You’ll have to wire up a switch to disconnect your amplifier when you want to use head phones. Or do what I did, use the pigtail. Then you just unplug the amp and plug in your headphones. And plug the amplifier in again when you want to switch back to speaker.
Another option is to try and find a breadboard friendly tip ring sleeve jack with the cutout function and wire that in between your speaker amp and Pi, and plug your headphones into that jack.
And wire it up on something like this