present with external bluetooth speaker

iPhone 14 Pro Max with iOS 18.2.1 and the Lightning connector for HDMI. I'd like to present (screen) via HDMI with sound sent to an external BlueTooth speaker. In other words, I don't want to send sound to the HDMI device.

With only BlueTooth connected, sound comes from the BlueTooth device. When I plug the HDMI cable in for screen, sound moves from the BlueTooth device to the HDMI-connected device, along with the screen.

I can separate HDMI video and BlueTooth sound on my Mac. Is this possible on an iPhone?