Expression.Error: We cannot convert the value #date(2023, 1, 2) to type Text

Looking again there appears to be an additional issue
is this [#"UK Holidays.Date"] meant to refer to itemss in this list: Table.ToList(#"UK Holidays") ?

If so try this instead:
List.Count( List.Select( Table.ToList(#"UK Holidays"), (x)=> x >= inicial and x <= final ))

if you're still getting a type conversion error, break your formula down and return each component to validate that it is returning the correct value and type you require. I find that nesting a record is a convenient way to do just that, that will look something like this.

Table.AddColumn( #"November days", "November holidays", each
    [
        h = Table.ToList(#"UK Holidays"),
        i = inicial,
        f = final,
        a = List.Select( h, (x)=> x >= i and x <= f ),
        b = List.Count( a )
    ]
)

When the record is returned, click off to the side in the whitespace to see its content, in an additional preview window below the main one.

I hope this helps you to resolve it.