Honestly, the most practical solution for a 4.4.4 Android TV is to buy a $20-30 external streaming stick (Fire TV Stick Lite, Chromecast with Google TV, or an Onn 4K box). These run modern Android 12+ and will give you a fully functional Play Store.
If you are determined to keep using the stock system framework, you must manually install the final stable builds released for API 19. They will not restore full store functionality but will fix background crashes on older apps that depend on fundamental Google APIs. The absolute ceiling versions for Android 4.4 KitKat are: Version 32.7.13 . google play store for android tv 4.4.4
Download your desired legacy TV applications from a PC browser. Honestly, the most practical solution for a 4