Thank you for your answers -
I ended up contacting Google support for assistance on this but I thought I'd provide my resolution for anyone coming across this in the future.
The client had a Google workspace account, which means many sharing settings are controlled in the Google Admin Console. This may be my fault for not disclosing this but I didn't think of it at the time being.
Go to your Google Admin site > apps > Google workspace > calendar > Sharing settings. From here, you should be able to edit external sharing (outside of your Google workspace) to your liking; the changes will take a few minutes to apply. Make sure to remove and then re-add the calendar after you've changed the global sharing settings.