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It's not that "tags appear to become meaningless once a newer version of a package is present", it's just that tags are part of an individual package's metadata (see the NuSpec Reference) just like name, description, authors, etc.
The VS Client, nuget.org, and every other package manager UI we've worked with will only do metadata search on the most current version of a package by default; otherwise, outdated and irrelevant packages would come up in results.
As you can see, it's possible to use an API to search for these things... but tags are simply not intended to solve the problem I think you're trying to solve.