Summary

After /provider <name> switch, the confirmation message and /provider status display the provider type (e.g. openai) instead of the configured name field (e.g. mini2).

Reproduction

[[llm.providers]]
name = "mini2"
type = "openai"
model = "gpt-4o-mini"

/provider mini2
→ Switched to provider: openai (model: gpt-4o-mini)   ← should say 'mini2'

/provider status
→ Name: openai   ← should say 'mini2'

Root Cause

handle_provider_switch and handle_provider_status use self.provider.name() which returns the provider type string (e.g. "openai"), not the configured name field from [[llm.providers]]. The list handler uses entry.effective_name() which correctly returns the configured name.

Fix

Store the configured name alongside the active provider instance (e.g. in self.runtime or a wrapper struct). Use that name in the switch confirmation and status output instead of self.provider.name().

Impact

MEDIUM — confusing UX when using named providers. Correct provider IS selected (routing and inference work correctly), only the display name is wrong.