Reorder persistence features

Originally created by @intrigeri on #15280 (Redmine)

See #15265 (closed) for the desired design.

Feature Branch: perl5lib:feature/14594-asp-gui, iuk:feature/14594-asp-gui, persistence-setup:feature/14594-asp-gui, feature/14594-asp-gui

Edited May 15, 2020 by intrigeri

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