The FiLMiC Pro mobile app has been released in new version 6.12 and now supports "clean HDMI out", i.e. the output of the pure video signal without overlays. However, not directly via HDMI, since the interface on smartphones and tablets is USB-C or Lightning (on iOS) instead. So you also need a corresponding HDMI adapter. Apple devices can also output wirelessly via AirPlay.
The video signal from the FiLMiC App can then be used for example via HDMI Switcher like the ATEM Mini from Blackmagic Design in multicam live productions. With the help of a capture stick such as Elgato Cam Link 4K, the HDMI signal can also be used on the computer as a webcam alternative.
The maximum resolution or frame rate of the video signal is determined by the respective tablet / smartphone manufacturer. Apple's Lightning max 1080p can output 60fps, but USB-C can output 4K 60fps, compatible Samsung devices can output 4K DCI 60fps. The video output is activated in the FiLMiC App via Settings > Hardware. The possibility to output audio along with the picture is only available under iOS (audio via HDMI).
By the way, the 6.12 update also offers full support for DJI OSMO Mobile 3 and 4.