Be mindful that OpenFL (and therefore Starling for OpenFL) does not support JXR compression. You need to select “Hardware Compression” in TexturePacker’s ATF options, and make sure “Compress with JXR” is un-ticked.
For a specifically desktop target, which I believe you’ve mentioned yours is, you should only enable “DXT” compression. The others can remain un-ticked, as these are for various mobile targets.
Now in terms of quality, for the game assets you’ve given examples of here, I think you’ll be fine. But, ultimately you need to be the judge of that, so the proof will be in testing and your judgement.