Just tried, searching the web page (fdroid.org) gives even 0 results.
Thesis: the app searches the app description texts, where you need to mention "codeberg" to pop up.
However, this is not the place to put the repo homepage, because there is an extra field for this in the app metadata.
Obviously, this field is not part of the search.
Conclusion: searching for "codeberg" in the app is not suitable to get reliable data on project hosting.
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