This is not the helpful answer you were looking for, sorry. I’m fairly certain that the consensus among data hoarders is that the answer is more storage space not smaller files.

You can absolutely re-encode h265 video, but you can’t do it losslessly. In the end, it’s always a balance between quality and filesize.

I decided for myself, that 1080p30 crf28 h265 is good enough for home video, which lead to a 50% to 80% storage space reduction on videos from my phone.

If you don’t obsess over quality, I would highly recommend just messing around with ffmpeg a little bit and decide how much quality you’re willing to lose in order to save disk space. When you’re happy with your settings, you can either use ffmpeg itself or some fancy batch program like Tdarr to transcode all (or parts of) your video library.

My goto command is:
for file in *.mp4; do ffmpeg -i "$file" -movflags use_metadata_tags -map_metadata 0 -vcodec libx265 -crf 28 -vf scale=1920:-1 -r 30 "${file%.*}_transcoded.mp4"; done

You will not gain much from reencoding or compressing these kinds of files. They are already compressed in a way purpose-built for their application. If you have source materials, like blu-ray discs, you can reencode with more aggressive h.265 settings. But this will probably not do better than shrink 5-30%.

It is usually a better use of time and resources to get more storage.

Offhand I think AV1 is supposed to be a bit better than H265, but I think the improvement would be pretty marginal. Also, that’s a newer codec with less support everywhere, so you might find yourself slowing down a lot doing live transcoding to a format with better support like H265 or H264, depending on your devices. Add in all the time transcoding your current files from H265 to AV1 and it might just be worth adding more storage space.

I have a lot of artworks I downloaded over years that were saved in png files and after converting them loslessly to avif I still was able to regain some space.

For videos you cant afford lossless if you want to recover space but visually lossless results are usually good enough on AV1

I converted my old phone photos to JXL for this reason. It is malpractice that Android isn’t doing this by default for all users right now.

I will use AVC and HEVC terminology for h264/x264 and h265/x265 respectively.

For video, you get jumps of compression quality from AVC to HEVC, from 8-bit to 10-bit, and from HEVC to AV1.

Depending on your source material, changing compression settings, like target quality, variable bitrate, etc, can also have significant gains. It will depend on your source and target though, and may need some testing to get “right”. If you’re looking for the best compression, that may be on a file by file basis, because different kinds of video have significantly different compression behavior or concerns. That’s likely not feasible for a mass of files though.

Playback compatibility should also be considered. AVC mp4 is the most compatible, right now, if you consider all kinds of and older mobile and embedded devices. If you’re fine with modern or desktop, you can go for the best compression codecs.

To get an idea of encoding time investment and quality, you can use ffmpeg with default quality settings, and target the different encoding targets.

AV1 10-bit, Opus audio:

ffmpeg -i input.mp4 -c:a libopus -c:v libsvtav1 -pix_fmt yuv420p10le out_av1-10bit-opus.mkv

AVC mp4 (when targeting mp4 these codec settings are the default, so in fact don’t have to be specified):

ffmpeg -i input.mp4 -c:a aac -c:v libx264 -pix_fmt yuv420p out_avc-aac.mp4

HEVC 10-bit, opus:

ffmpeg -i input.mp4 -c:a libopus -c:v libx265 -pix_fmt yuv420p10le out_hevc-10bit-opus.mkv