Just expend some more compute time on doing compression and we’ll get those filesize numbers to a workable level.

$ stat -c %s enhance.png 
276773
$ convert enhance.png enhance.avif
$ identify enhance.avif
enhance.avif AVIF 1164x558 1164x558+0+0 8-bit sRGB 14391B 0.000u 0:00.000
$ stat -c %s enhance.avif
14391
$

zoom and enhance

$ identify enhance2x.avif
enhance2x.avif AVIF 2328x1120 2328x1120+0+0 8-bit sRGB 32448B 0.010u 0:00.000
$ stat -c %s enhance2x.avif 
32448
$

zoom and enhance

$ identify enhance4x.avif 
enhance4x.avif AVIF 4656x2232 4656x2232+0+0 8-bit sRGB 50758B 0.000u 0:00.000
$ stat -c %s enhance4x.avif
50758
$

Okay, that last one took 17 minutes to upscale on my GPU, so I’m not going further. But I’m using SD Ultimate Upscale, which is tile-based, so in theory that could be farmed out over a collection of GPUs and parallelized. Just need more compute hardware.

But as to filesize, that’s under 50kiB.