Welcome to the Airtable community!
It looks like you want to fill in in the {Assignees} field in the [Main] table with a record from the [Assignees] where the company and category in the [Main] record match those in the [Assignees] record.
In Airtable, you cannot use a “lookup” for this. In Airtable, a “lookup” is for getting a related value in the same table as a linked record.
Instead, it looks like you want to create the initial record link (although you currently have a single line text field for the assignee).
One way of doing this is with scripting.
If there will only be one company and one category in the [main] record, it could also be done with an automation and a “find records” action. However, it looks like you have multiple linked records in the {Category} field, and the “find records” approach will not work.