Bluetooth headset and audio while using hdmi output from iphone 15 pro

Hi there everyone!

I'm trying to solve a problem related to bluetooth audio and hdmi out from an iphone 15 pro for a friend so we can watch movies together and talk over discord at the same time. I'm fine on my end, but I need to figure out for the friend if purchasing a USB-C to HDMI cable will allow her to output to fullscreen on her TV AND allow her to wear bluetooth headphones and talk through the accompanying microphone on them to me (via discord running on her iphone simultaneously).

Her TV does not have bluetooth, so the option to simply pair with the TV is not on the table.

Not being an apple guy, I can't confirm it on my end, so I'm asking the community.

Can the individual output from USB-C to HDMI from an iphone 15 pro and use bluetooth pairing from the same iphone, such that she can discuss and talk with me on discord (running on her iphone simultaneously in the background) while watching stuff on her TV (which receives the HDMI output)?

Essentially, we want the audio to not play through the TV. We want the picture of the iphone to display on her TV and then we want to hear audio from the iphone on her bluetooth headset, which she'll simultaneously use to talk with me on Discord.

Being a typical PC user here, I know it's possible on my end, but finding the right forum post on the net explaining this situation has been difficult. I'm sorry if this has been asked and answered before and I appreciate any help!

-- Matt