I understand that you're trying to update the Jira Software application from within the Jira web interface (Cog Icon -> Applications -> Versions & Licenses). However this method to update Jira Software is dependent upon having specific versions of Jira Core already installed. You don't need to license Jira Core as long as you have either Jira Software or Jira Service Desk licensed.
I would be interested to see if you can go to that page listed above /plugins/servlet/applications/versions-licenses and then scroll to the bottom to see what specific version of Jira Core is current installed. You can find this either in the footer or in the Jira Core entry listed there. I would only expect that you could install Jira Software 8.4.2 to a corresponding Jira Core 8.4.2. And in order to install that you'd need to actually stop Jira application itself and then perform one of the upgrade methods in Upgrading Jira.
While investigating this issue, I came across the version history page in marketplace https://marketplace.atlassian.com/apps/1213607/jira-software/version-history
I found something unexpected here. It seems that currently Jira Software 8.4.1 is shown as compatible with 8.4.1 - 8.4.3. This is unusual given the other entries here, most everything else here in recent history has had a 1:1 correspondence with Jira Core versions. Right now I can't explain why this version is not 1:1, but 1:many here.
I'm going to raise this concern with my team to see if this is intentional or perhaps see if this is an oversight on our part. It might explain why you see the option to update this in Jira, but it then is not working to actually update this.
I will let you know more once I have an update.
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