Yeah, I was never able to get Perl::LanguageServer to work on 64bit Strawberry, either (though it looks like you tried harder than I did).

PerlNavigator works with my Strawberry v5.38.0 for MSWin32-x64-multi-thread. Its homepage gives examples of how to set it up for VS Code, Sublime, emacs, neovim, and others... And it is starting to work with an alpha NppLspClient plugin on Notepad++, using the config below:

[lspservers.perl]
mode = "io"
executable = 'c:\\usr\\local\\bin\\perlnavigator.exe'
args = '--stdio'
auto_start_server = true
[download]

The upsides are that PerlNavigator uses the Microsoft LSP library, so is known to work well on Windows; and it doesn't have difficulties installing module prerequisites, because it's a standalone app, not a Perl-based application or module(s). The downside is, it's not a Perl-based application or module(s) ;-).

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update: sorry, I hadn't seen haj's post yet when I replied to this one. but mine does include tangential information which might be of use to non-VSCode users wanting similar functionality on other Windows editors.