When an user is assigned to a ticket which is still in open status, then the other users/project admins shouldn't be able to assign that user to another tickets. Is it possible to achieve this using any technique/method?
No, there's no way to do that.
You could do it if you were using DC though, but you'd need to rewrite and recompile bits of Jira to do it.
There is definitely a workaround which you can use to achieve this. It might not be straight forward but it gets the job done.
The approach I would take is basically creating an automation, listening to the assigned trigger, checking if the assignee already has open ticket(s), then add a comment saying that the user has other commitments (optional), and finally unassign the issue.
This is basically your own custom validator like automation.
Here is a screenshot which you can use as a draft:
Hope it helps!
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