The re-use tab in the reference dialog allows searching for group names. This was always possible. However, it doesn't work when the group name is uppercase or contains an uppercase character. For example, it works when the group name is "note" but not when the group name is "A". It doesn't matter if I search for "a" or "A", it's not found.

Turns out the relevant code is incomplete ever since it was written in 2013, see https://gerrit.wikimedia.org/r/70364. The relevant ticket was T51733: VisualEditor: Support creation/editing of references using an existing ref-name.