1. Similar looping behavior
2. No audio
3. Can be put in an <img> tag
You should be able to save the file like you would a gif, and viewers should also show it as they would a gif (not a video).
HEIF is an ISOBMFF (aka Quicktime/MP4 container)-derived container format for images, image sequences, and transformations. Its most visible use right now is Apple Live Photos, but various use-cases exist . OS and application support is increasing.
Work is ongoing on defining AV1-encoded frames as a payload in HEIF .
 https://nokiatech.github.io/heif/technical.html  https://nokiatech.github.io/heif/examples.html  https://aomediacodec.github.io/av1-avif/#av1-image-sequence
The patent or patent application numbers, in order of their appearance in these documents:
AU 2014255577, CA 2909566, CN 201480034418.2, EP 14785343.6, IN 6931/CHENP/2015, KR 2015-7032685, RU 2015146961, US 14/254120, US 14/617266, WO PCT/FI2016/050063, US 14/618650, WO PCT/FI2016/050064, GB 1418114.3, WO PCT/FI2015/050671, WO PCT/FI2014/050582, US 14/583332, PCT/FI2014/051052, PCT PCT/FI2016/050381, US 15/578288
This is where I'd start.
 https://mpeg.chiariglione.org/patents  https://isotc.iso.org/livelink/livelink/fetch/2000/2122/3770...  https://isotc.iso.org/livelink/livelink/fetch/2000/2122/3770...  https://isotc.iso.org/livelink/livelink/fetch/2000/2122/3770...  https://isotc.iso.org/livelink/livelink/fetch/2000/2122/3770...  https://www.iso.org/iso-standards-and-patents.html
https://patents.google.com/patent/US20160234144A1/ This one seems to be about specifying a Mimetype paramater that tries to describe the cost of image transformations requested in the target file, so that clients who know they can't perform those transformations can pick a different file.
https://patents.google.com/patent/US20160232939A1/ Seems to be about image sequences and specifying such a concept with coherent metadata in the container.
https://patents.google.com/patent/US20150193494A1/ This seems to talk about the myriad ways that ISOBMFF can assert metadata about data elements within, but there aren't always good ways to ensure the metadata points back to a specific data element. This talks about ways of figuring out whether such loosely-floating metadata in the container is still valid for data items; they also propose using checksums to figure out if the data items changed.
https://patents.google.com/patent/US20180146225A1/ This is a fancy restatement of P-frames for still images, leaving open the possibility that later frames also 'enhance' the first image in various ways e.g. upscale resolution and others.
https://patents.google.com/patent/US20140314148A1/ This defines signalling to allow putting all the I-frames at the start, and all the P-frames at the end.
So that solves that problem.
Which other patents is HEIF encumbered by?
Licensed Field is defined to be: "(...) the non-commercial purposes of evaluation, testing and academic research in each non-commercial case to use, run, modify (in a way that still complies with the Specification) and copy the Software to (a) generate, using one or more encoded pictures as inputs, a file complying with the Specification and including the one or more encoded pictures that were given as inputs; and/or (b) read a file complying with the Specification, resulting into one or more encoded pictures included in the file as outputs."
It is pretty clear from this reading that their patent grant is for non-commercial evaluation, testing and academic research only.
Again, AV1 is royalty free, not patents free.
There is a feature request for Chrome: https://bugs.chromium.org/p/chromium/issues/detail?id=791658