Does Apple allow developers or testers to install previous versions of an App? As an iOS App developer, does Apple allow me to download previously submitted versions of my App using a developer or test account?

I'm not trying to get users to download previous versions, but instead I need to reproduce issues on older versions of the app.

I assumed each submitted version uploaded to App Store Connect would show a link to download/install the App, but there doesn't seem to be anything.
No, this is not allowed.  You can only have 1 version available for download in the App Store at a time for a specific iOS version (users with older versions of iOS can download the last compatible version of your app but I don't think that's what you're looking for).

I'm not sure if you can upload a lower version to TestFlight as I've never tried it.  If it works, you can limit the ability to download it to specific users.  That might achieve what you're looking for.  Maybe someone can [edit] this answer if they know this is allowed.