Thank you for your response.
I can confirm that you could achieve this requirement using ScriptRunner for Jira Cloud and by writing a script Listener script which is configured to run on the comment created event.
The script would then need to check if the comment author matches the assignee of the ticket and if it did not to call the Update Comment API which Atlassian provides to set the author of the comment to the assignee of the issue.
I hope this information helps.
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