awk pickle

Hi I am trying to write a proper awk statement to only return hostname entries from a logfile from a week ago to present time.

Logfile format is like this:
27-04-2024_00:04 hostname1 EverythingElseAfterHere
28-04-2024_02:05 hostname2 EverythingElseAfterHere

I thought I could reformat the date to a single string and compare like so:

#!/bin/bash
# get the date from a week ago:
lastweek=$(date +"%Y-%m-%d" --date="1 week ago")
# run today (5/1/24), this returns:
20240424

Then I tried converting field $1 in my file via awk to a similar format:
awk 'n=split($1,a,"[-_]") {print a[3] a[2] a[1]}' mylogfile
# this also looks good, returning as an example:
20240427

Here is where I get stuck. I want to (if possible) use the value of n to compare with lastweek and see if the date (value) is greater:
awk -v lastweek="$lastweek" 'n=split($1,a,"[-_]") {print a[3] a[2] a[1]} n > lastweek {print $2}' mylogfile
# this just returns more dates like '20240427' but I want field 2 with the hostname

I don't even know if I am doing the compare correctly or if its even possible.
I am trying to push the output from the split/print subcommand into 'n' and then compare that timestamp as text to the lastweek text and if n is greater then output $2 (hostname). Its getting messy and I am getting confused now as I am not very familiar with awk.

Any help would be greatly appreciated.

Thanks!