Search persons by SharePoint lookup column values in Power Apps

I have a SharePoint list and it has a lookup column called "Skills" that can save multiple values and a person column which stores Microsoft 365 users.

This SharePoint list is connected to canvas Power Apps. I need to implement a feature that can filter persons by searching the skills.

How to implement this?

This is a preview of my SharePoint list:

This is a preview of my canvas Power Apps:

This is the current search formula to search by person name.

Filter(
    Skills,
    Or(
        StartsWith(
            Employee.DisplayName,
            SearchInput1.Text
        )
    )
)

Filter(
    Skills,
    Or(
        StartsWith(
            Employee.DisplayName,
            SearchInput1.Text
        ),
       CountRows(
        Filter(Skill, StartsWith(Value, SearchInput1.Text) )
       ) > 0
    )
)