The provider-chain summary marked every entry available, so the Coach's
provider select offered entries without a key or sign-in. Choosing one
saved it to the front of the chain, the resolver skipped it, and the
select jumped back without a word.
Availability now comes from the presence probe, which names every chain
type whose credential is present. After a switch the picker reads the
chain back and says so when the server still answers with another
provider.