Free and Open Source Software

ffmpeg is usually the tool of choice.

An example for batch converting of all AVI videos in a folder:

for i in *.avi; do ffmpeg -i "$i" "${i%.*}.mp4"; done

Source & further reading here on StackOverflow. The comments to the answer provide examples of how to explicitly tweak the quality level. Inverting what this specific comment suggests, conversion from H264 to H265 could be done by something like this, assuming all your videos' names end on .mkv:

for f in *.mkv; do ffmpeg -i "$f" -map 0 -movflags faststart -c:v libx265 -c:a copy -c:s copy "${f/x264/x265}"; done

I wonder: if one wants to make things run in parallel, would that be as easy as adding " & " before the last semicolon here? I suspect this could work as long as there are only a few handful of files, but lead to troubles once there's more.

You're wrong about not being able to levelage your Intel graphics. Intel 11th gen has hardware HEVC (h265) encoding. Your Samsung phone probably also has HEVC hardware encoding faster than your CPU encoding. You want the ffmpeg hevc_vaapi codec, and it should go even faster if you use -hwaccel vaapi for decoding.

FFmpeg is your friend. Here's a command that should work:

mkdir converted; for i in *.mp4; do ffmpeg -i $i converted/${i::-3}.hevc; done

It won't get much faster than properly used Handbrake.

Didn’t ffmpeg just post another huge speed gain?

Ffmpeg