Don’t give your TV internet access, and use an Apple TV.
This is probably obvious to most people, but I will mention just the same: do not install the antenna that the TV comes with.
Wifi antennas would typically be internal and unrelated to the one F-Type coaxial connector one would typically think of as the "antenna" input.
Can't really stop the internal module from scanning and connecting to open access points unless you control the software.
Exactly this. Search for a mini PC and it'll have a cheap Intel SoC in it that performs way better than a Raspberry Pi 5 but cheaper (comes with everything for ~$300), and even consumes a similar amount of power.