I don't Wanna Lose Any Data...
Okay that makes sense.
But With Thousands of Frames in 4K File Size Matters.... So Why not Encode to H265
That makes sense in a vacuum, but it's incompatible with the initial goal. The reason that H.264 or H.265 is so much smaller than your initial image sequence is because those codecs use lossy compression. You can't make such a conversion without losing any data, even before we get to the fact that H.265 doesn't support 16 bit RGBA formats.
You need to figure out whether your goal is to make it as small as possible, or to preserve all of the data. Those are mutually exclusive goals.
It's also worth considering what you are actually planning on doing with your rendered frames. Does your editor even support 16 bit RGB internally, or is it converting to something else as a working space? Are you ultimately outputting to a destination format that will preserve the quality? And if not, are you doing any color corrections or effects in your editor that actually benefit from having it during the intermediary steps?
In a VFX studio, a typical workflow would be to render to EXR images, then post process those EXR images so they have lossless compression, and any black void are in the image is cropped so the data window is only a subset of the display window. Then use those optimized EXR frames directly in compositing or editorial rather than making something like a QuickTime or MP4 file as an extra step. You can use something like oiiotool to autocrop the EXR files.