Send Files to TV, the easiest way. https://play.google.com/store/apps/details?id=com.yablio.sendfilestotv
There is a windows client for Send Files To TV.
Try another browser like TVBro
Why not just use Downloader by AFTVNews?
Windows firewall blocking BlueStacks? Try disabling temporarily.
Are you on the same wifi network?
Bluestacks would create its own separate network
Try TvBro and search for the legacy Firefox Android TV app from there. I'm not sure but I think it's the Amazon version. Regular Firefox wouldn't install for me a couple of days ago and I sideloaded Samsung Internet instead.
why not adb?
I installed X-plore File Manager on my TV, and let it access my could storages to install apks saved there.
Use Bugjaeger. I sideload everything with this from my phone to tv with ADB, no cables or PC needed.
Use a windows share device, download xplore on the tv and go to lan part, there you can scan your lan and find your share. Easiest way to install apps on android.