I took a photo with the camera that is shipped with my phone (Samsung with Android 10).
This format has the advantage of a smaller file size.
Steps to Reproduce:
Open Writer or Impress. Next try to insert an image by selecting all types of files.
I get an error message which tells the format is unknown (French localisation).
Display the image into the document.
User Profile Reset: No
I tested on GNU/Linux x86_64 with 18.104.22.168 version. However, the bugs appears with an older Lo version on Microsoft Windows.
There is currently no import support for HEIC image format. You'll need to convert external to LibreOffice.
I see filter import of HEIC "HEVC in HEIF" compressed image format as counterpoint to AVIF "AV1 in HEIF" of bug 138668
The AV1 is more appealing for license, but HEVC is probably more common.
If libs and license allow, probably both should be implemented.