fix: use previous_response_id chaining for OpenAI store=true follow-ups (#23450)

OpenAI Responses follow-up turns were replaying full assistant/tool
history even when `store=true`, which breaks after reasoning +
provider-executed `web_search` output.

This change persists the OpenAI response ID on assistant messages, then
in `coderd/x/chatd` switches `store=true` follow-ups to
`previous_response_id` chaining with a system + new-user-only prompt.
`store=false` and missing-ID cases still fall back to manual replay.

It also updates the fake OpenAI server and integration coverage for the
chaining contract, and carries the rebased path move to `coderd/x/chatd`
plus the migration renumber needed after rebasing onto `main`.

coderd/database/models.go

@@ -4229,6 +4229,7 @@ type ChatMessage struct {
 	TotalCostMicros     sql.NullInt64         `db:"total_cost_micros" json:"total_cost_micros"`
 	RuntimeMs           sql.NullInt64         `db:"runtime_ms" json:"runtime_ms"`
 	Deleted             bool                  `db:"deleted" json:"deleted"`
+	ProviderResponseID  sql.NullString        `db:"provider_response_id" json:"provider_response_id"`
 }
 
 type ChatModelConfig struct {