I never want to get a smart TV, but I found this exact TV (Toshiba FireTV) on the side of the road and decided it would be a fun project to try enhancing its privacy as much as I can. It did not come with the remote or any other accessories besides the TV, so if there is any way to pair an iPhone/Pixel as a remote that would also be good. Is there any way to replace the software with something open source, and anything else I can try?
You can get an Apple TV, which is an external device you connect to your TV if you're already in the apple ecosystem. You can use your iPhone as a remote for it.
There is also the Nvidia Shield option, which is a solid Android TV option.
And of course, you can just use any pc as an input device and use that.
The firmware thats actually on the "smart tv" might be tough to replace with an open source solution. Im sure there are some TV modders out there, but its probably very niche. Best to get an external device of your choice imo.
It did not come with the remote or any other accessories besides the TV, so if there is any way to pair an iPhone/Pixel as a remote that would also be good.
Infrared remote control sequences are often shared by multiple models, sometimes even across multiple brands. If you can't find an exact replacement on ebay, it might be worth trying a remote from a different model released within a few years of this one.
Also, remote codes are often captured for various TVs and preserved as config data for use with projects like LIRC. Someone out there might have the data for this model. Some universal remote controls will even have the codes for popular TV brands pre-programmed into them.
While I agree with you, if OP is spending money on a remote, they may as well try to find an original remote. They're unlikely to be expensive, and will have all the correct buttons :)