refactor(core): move database schema ownership (#29068)

Co-authored-by: copilot-swe-agent[bot] <198982749+Copilot@users.noreply.github.com>

packages/core/src/provider.ts

@@ -22,6 +22,9 @@ export const ID = Schema.String.pipe(
 )
 export type ID = typeof ID.Type
 
+export const ModelID = Schema.String.pipe(Schema.brand("ModelID"))
+export type ModelID = typeof ModelID.Type
+
 const OpenAIResponses = Schema.Struct({
   type: Schema.Literal("openai/responses"),
   url: Schema.String,