I avoid syncing photos to the cloud, I take far far too many to waste the bandwidth and time uploading them, and no free service would give me enough room (I can easily take 1000 in a day if I'm taking pics in the afternoon and then also the moon at night). I do however have my own extra hard drives that a program automatically runs nightly to back everything up. And then periodically that's backed up onto a 3rd drive. I have decades of photos that would kill me if I lost them. A HD you control completely... you can't control someone else's cloud service or its reliability or if it won't close one day.
When you say syncing, which program? Is it an HP included program? Or Google's cloud service? That will help someone else who might use the same one as you.
Depending on what time (meaning how many hours into the moonrise, which will vary nightly), you will see a slight rotation of the moon. I typically see as much as a 30° rotation (just a guess, I didn't measure from photos). If you download an app that shows the phases of the moon, you'll easily see the rotation by just sliding your finger to change the time. Phases of the Moon by M2Catalyst LLC is the one I prefer for my Android devices.
To me, the first 2 pics look pretty typical for being 2 days away from a full moon. The first image here is 2 days before the full moon on 7/11/22 about 10:30 central time. The 2nd image is on 7/13/22, the night of the full moon, around 11:30 central. If I use layers to place them on top of each other, I can see a slight twist in position for all the craters, even though just 2 days apart, the time should be pretty close, and it also makes the dark left side much more apparent.
Taken 2 days before the full supermoon:
Taken the night of the supermoon:
Edit: Here's one from 3/1/18 that probably a day past the full moon. Notice where Tycho is (bottom right side that looks like the navel of an orange). Everything is tilted compared to the others.