How can I restrict JIRA issue update/edit only for Assignee(irrespective of Project Roles)
Look at the permission scheme for the project.
Find the lines that control the edit access (most important is probably "edit", but there are others you might think of as "updates" or "edits").
Remove all groups, roles, individuals etc, leaving JUST the assignee in those lines
Secondly, assuming "move issue to new status" needs to be controlled as well, go into the workflows and check that the "conditions" on transitions you want to restrict to the assignee only all say "assignee only"
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