If this was on the same Cloud URL, you could just use the built in Automation for Jira Service Desk to automatically create a new request in a different project when the approval is completed. This would be the easiest way to do so.
However since it sounds like you're using two different URLs for your different Cloud sites, this specific option in automation won't be possible directly. You can probably still using automation of Service Desk to help here though. But using webhooks to do this isn't really ideal. The webhook can do a POST of sorts, but it wouldn't be a great simple way to link this back to the other issue. I suspect you want some way to link the description/title of the original issue with the newly created issue.
Instead, I'd go with using automation trigger rule of 'Approval Complete' and then automation action to 'Send Email'. Then set this up to send to the inbox of your other Jira project. This method presumes that your other project has an email address/mail handler setup for it to accept incoming messages and create tickets as such. If you are not familiar with doing this, I would recommend checking out the Automating your service desk for some more background on this topic and how you can use this built in feature to Service Desk to accomplish this.
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