The server and the composer share the rule, in lastUsedModel and inheritedModel. The composer's model select shows a chat's own model by name, offers "Default" only before the chat has one, where it means the default from settings, and shows a loading line while the chat's messages are on their way. Each message names the model that answers it, even one left to the default, and Regenerate and Try again send the reply's own model, so a changed default or a sibling's model never takes its place.