$icon =~ s/https:\/\/api.weather.gov\/icons\/land\///;

This substitution needs more backslashes (escapes)! (Never thought I'd say that.) The regex  . (dot) operator matches, by default, any character except a newline. E.g.:

c:\@Work\Perl\monks>perl -wMstrict -le
"my $icon = 'https://apiXweatherXgov/icons/land/fooble';
 $icon =~ s/https:\/\/api.weather.gov\/icons\/land\///;
 print qq{'$icon'};
"
'fooble'
[download]

To match only a period, escape the dot metacharacters:
    $icon =~ s/https:\/\/api\.weather\.gov\/icons\/land\///;
Of course, a dot also matches a period and that's all that seems to be in those particular positions in your strings so you might never have known the difference, but just for future reference...

BTW: One way to cut down on escapes in a regex is by the wise choice of a regex delimiter. E.g.:
    $icon =~ s{https://api\.weather\.gov/icons/land/}{};

Please see perlre, perlretut, and perlrequick.