Are you aware of Row level security in Power BI? It seems exactly what you need. You can hold the report for all users in your group, add the users in the group(member read) and assign them proper roles. Then no effort is required on automation.
Regarding "System starts creating the reports with the modified parameters to reflect the client's user", as far as I know, so far there's no approach to access and modify a pbix file programmatically。