@AjvadK
The existence of field level ACLs on all fields makes this more complicated. In order to achieve your exact use case you will need to modify every field level rule to achieve exactly what your use case implies. How you modify each one is going to depend on the more specific requirement for access to that field. First keep in mind that the table.* rule still needs to provide access so the script logic would need to be added as an OR condition on it as well as modifying the field level ACLs.
If you need the existing write rule to work as it is written but also add any assignee then you can add an OR condition with the scripted logic provided earlier.
If you need the field to be write only for the assignee and no one else then you would need to remove the current associated roles and add the scripted logic.
If you need the field to be read only for everyone then you need to remove the existing business rule so that there is no field level rule for that field.
If there are only specific forms or areas where you need these permissions restricted then there are some more specific approaches for that such as using display rules to override the edit privilege. These are not considered secure as they can often be manipulated on the client side but depending on if these rules are required for security purposes or just user experience you might have an easier time going with ui policies and display rules.
