You can do this whether you are using a GPIO sound card or USB sound card. It may be better to use a GPIO sound card short list here, because it will have less latency then blocking out to USB using UAC2... But that remains to be seen.
Before I launch into how to implement this, have you considered using a sound card with both headphones and RCA outputs? If you are happy to take input to your TV from the RCA jacks, that may be neater, with fewer clock drift and format problems. Some of the listed GPIO sound cards have that feature.
You need to create an asoundrc which copies audio to both sound cards using ttable.
ttable.0.0 1; # Map card 0 ch0 to ch0
ttable.1.1 1; # Map card 0 ch1 to ch1
ttable.0.2 1; # copy audio from 0 to card 1 first ch at full vol.
ttable.1.3 1; # copy audio from 1 to card 1 second ch at full vol.
Beware as you may get clock drift between the cards and various other formatting issues. To get around this, investigate using plughw as the device when defining the card in the
slaves.a.pcm line and equivalent for b. Something like
card0 is your actual card. This info can be found using the
aplay -L command.