VLOOKUP with date range does not work as intended

Question

I have two excel tables in separate sheets:

table1:

Site_ID ....... Visit_Date
--------------------------
AS01            12-Feb-23
ES96            10-Jan-23   
GH15            14-Mar-23
AS01            26-Mar-23
VD10            08-Apr-23
LS18            14-Jan-23
GH15            26-Mar-23

table2:

            01-Feb-23   01-Mar-23   01-Apr-23
            28-Feb-23   31-Mar-23   30-Apr-23
Site ID         FEB23       MAR23       APR23
---------------------------------------------
AS01
ES96
GH15
VD10
LS18

If the date falls within the acceptable range indicated above the table2 heading, I want to look for the Site ID in table1 and insert Visit Date in table2.

I tried the following formula:

=VLOOKUP(table2[@[Site ID]:[Site ID]],IF((table1[[Visit_Date]:[Visit_Date]]>=E$1)*(table1[[Visit_Date]:[Visit_Date]]<=E$2),table1[[Site_ID]:[Visit_Date]],""),12,FALSE)

Unfortunately, the FEB23 field produces dates that are out of range, and the remaining columns yield value errors. Why am I misusing this?