Sid's decision: the setup chat installs for the profile the user will
work in, where start_chat sends the task, not into the setup profile.
- default_target_profile() is the chat's own profile, except when that
home carries the setup-profile marker; then it is the launch profile
(server._hermes_home). Every other chat keeps the chat's own profile.
- prepare() and search() use it, so the card row, the install and
search's installed_in agree. The card still shows the target, and
Advanced still picks another profile.
- The manage_catalog description and the reference docs say where the
setup chat installs.
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