It would probably be easier to just build a media server pc that can be housed somewhere in the house, and then use two Raspberry Pi's or two network media players connected to each tv to stream the content from the server.
You could drive both tv's off one pc however, if you want to watch something on both pc's at the same time you will run in to issues due to audio, as you won't iirc be able to specify which audio output each piece of media uses, but I have not tried doing that so you might be able to but it would probably be abit fiddily.
I used one of these
WD units until I got my 3D Smart TV, and that little WD unit had no trouble playing content from my pc over wireless and also was fine with Netflix, Youtube and Radio.
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7900X3D, 64Gb Corsair 6000Mhz, Gigabyte Aorus RTX 4080 Super, Samsung 980 Pro 2Tb NVME
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