802.11n (Wi-Fi 4, 2009) should still be able to deliver ~65 Mbps per Wi-Fi channel, so plenty enough for 4K HDR streaming, which often maxes out at 25 Mbps. Assuming no meaningful obstructions, and not to many other devices consuming bandwidth on the same AirPort at the same time.
Can you do a Wi-Fi speedtest on the exact location of the TV, or maybe even through an app on the TV or TV-connected streaming device?
Newer routers and access points have a much easier time to deliver higher speeds to more devices and other optimizations, as well as increased security. Apple officially discontinued their whole line of AirPort devices in 2018, although their latest model was from 2013. An upgrade would be advised, imho, as your Wi-Fi use will be significantly different from 2009.