Hi @cosmas2. Welcome to GoDaddy Community! It looks like you may be hosted on a cPanel account. If so, you can update this setting within your cPanel dashboard. Take a look at this post, which explains how to add the zip module.
my cPanel does not have that option in the post you referred to. Below is what I see in my software section of my cPanel. I have new VPS deluxe server account i just switched over too this month
Did you ever get a response to this? I'm having the EXACT same issue and also have a VPS account. Did you figure out how to fix it? I've enabled what I thought it was in WHM but it still doesn't seem to be working.
I had the exact same problem, this article worked for me: EasyApache from your WHM panel 🙂 hope that helps.
NOTE: once you enable the options for the appropriate PHP version(s) your using (or just turn them all on) click next on the bottom of the screen/page until it asks you to process the update/changes. After clicking the process button be patient and allow it to run through the entire update.