What you’re describing is just compressing in a ZIP file. Zip files are lossless, you have nothing to worry about. When you throw a JPG in a zip file, and then extract it later, you’ll get the exact identical JPG back.
You only have to worry about jpg’s lossy compression if you’re using a photo editor like Photoshop, GIMP, etc. “Compressing” it in a zip changes nothing. Moving or copying it doesn’t lose quality either.
One of my favorites from Oh Bo by Bo Burnham:
Pull it out, stick it in your mouth, and I bust in the back of ya
Swallow bitch, there’s people starving in Africa