Would getting a separate AP improve my situation over AT&T fiber gateway/router?

I have AT&T gigabit fiber and am forced to use their gateway/router BGW210-700. It works good enough for wired connections (besides not letting you change DNS) but the Wi-Fi is mediocre.

I was looking into buying a Ubiquiti Access Point WiFi 6 Long-Range or Access Point WiFi 6 Professional. But I’m not ready to go all in with a UDM Pro and POE switch at this point. I’d just buy a POE injector for power.

Would this be a notable improvement if the AP still has to be placed in the same location as the AT&T gateway? I’m renting and can’t run cabling through the walls or mount an AP on the ceiling.

Edit

Also do you miss out on my not running the Unifi controller software on a computer? I wouldn’t have a Cloud Key or UDM pro, and was hoping to just setup and leave the AP running without the controller.