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Use the sound mixer and mute Galaxy?

You should be able to disable the sounds in Galaxy settings: go to Notifications and change any instance of 'Sound' to '-' in the right-hand column. There's also a volume slider at the bottom.

1. Click the cogwheel in the top left and choose Settings.
2. Click Notifications on the left.
3. At the bottom on the right, drag the Sounds Volume slider all the way to the left.

Alternatively, you can disable achievements altogether in the Game Features section of the Settings window.

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Okay, but why use Galaxy as a glorified screenshot maker when ShareX exists?

Or the Print Screen on your keyboard. But I'm not sure if it's something that every laptop has.

Okay the windows mixer resets the volume level for galaxy after a reboot (or maybe even after quitting and restarting galaxy, didn't test it).

The Galaxy settings -> Notifications -> Sounds are the way to go, works flawless. Galaxy creates a screenshot folder with subfolders in it for the each game you took a screenshot in.
Also ShareX looks bloated to me: https://getsharex.com/img/ShareX_Screenshot.png and it has goolag support. Same here: all screenshots in one folder, like snipping tool.

That said, it's pretty annoying that the Print Screen key can only take one screenshot at a time, which consequently would require me to exit the game to get that screenshot saved first, then reopening the game, and do it all over again if I took another screenshot. Snipping tool is also a good tool, but it's much more practical when you're not playing the game on fullscreen mode.
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Print Screen just copies a screenshot to the clipboard.
Windows logo + Print Screen will save the screenshot to a file, in the Screenshots folder under the Pictures folder. I don't know how well this works with 3D applications. Historically, generic screenshot utilities have had trouble with these.
Windows + Alt + Print Screen will save a screenshot to a file via the Game Bar feature in Windows. Files are saved in the Captures folder under the Videos folder. You can assign a secondary keyboard shortcut in the Settings app.

Wait, you mean in order for me to be able to take multiple screenshots using the Print Screen key, I need to press the Windows logo as well? Because what I've been doing is that I would only press the Print Key, head to my Paint program, paste the screenshot there, then save the file.

I can't make my post any clearer. Go to 2:44 in this video tutorial if you need to see it in action.

Got it. Thanks for the video!

there needs to be an option to auto upload and then delete every screenshot that you take.