For video, MV-HEVC (the Apple-pushed format) is probably the best bet, since it's both well-documented as a HEVC/H.265 extension and (because it stores diffs instead of full duplicate frames) it's way more practical for high-res and HDR video than previous de facto formats like side-by-side video. It's likely to be widely adopted by data hoarders, if only because it will save a huge amount of file space on 3D blu-ray rips.
Photos are more up in the air in part because the use and support of the Apple-pushed HEIC is much more limited than HEVC. But internally it's basically the same thing as MV-HEVC except with just the two still frames encoded instead of full videos, so any codebase that supports MV-HEVC should be able to support the 3D variant of HEIC as well without a lot of extra work over the long term.
Photos are more up in the air in part because the use and support of the Apple-pushed HEIC is much more limited than HEVC. But internally it's basically the same thing as MV-HEVC except with just the two still frames encoded instead of full videos, so any codebase that supports MV-HEVC should be able to support the 3D variant of HEIC as well without a lot of extra work over the long term.