As others have said, the problem is the mismatch between just "use webData" and "package MyPackages::Config::webData". The name you give to use has two purposes; one is to be translated to a filename for which to look, the other is to be the class for which the import() method is called. When you say use webData qw(GetLinks);, this is like:

BEGIN {
  require "webData.pm";
  "webData"->import( qw(GetLinks) );
}
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and since there is no webData package to call import for, no importing happens.

Since you seem to say the long package name is a necessity, the easiest solution is to change your filenames to match, so you have:

/myApp/cgi/login.cgi
/myApp/config/MyPackages/Config/webData.pm
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and do use MyPackages::Config::webData qw(GetLinks);.