I generally upload a new version of the package, usually with the version number added to the name. And then replace the package in the poilcy. When I am ready to go, I simply view the logs and hit the Flush All button, and the policy will rerun with the new package.
I keep old package versions for a while, just in case I need to revert back.

Try using the Jamf App Catalog for updating as you don't need any Packages.

The clone button is your friend. I tend not to flush any logs in case I want to see logs. But I'll do a weekly clean-up on very old policies and packages.

Someone also mentioned it, but Jamf App Catalog or Installomater are good options if your organization allows. Great options if you're not tied to tight version control.

Thanks for the suggestions. I guess we will have to use one of the suggested options with either replacing the package in the policy or duplicating the policy with the new package

Since, at the moment we can't use the Jamf App Catalog since we have on-prem Jamf (but we are probably gonna change to cloud when it's time to renew).

We have been using Installomator for some software, it is a neat script. It's just some softwares aren't in it unfortunately.

Depending on the software title/s, you might be able to get them added to Installomater.