TypeScript Type Incompatibility Issue with `extend` and `omit` in Schema Definition

import { Schema as S } from "@effect/schema";

type Model = {id: string} & Record<string, unknown>

const makePatchSchema = <T extends Model>(schema: S.Schema<T>) => {
  type Patch = Pick<T, "id"> & Partial<Omit<T, "id">>;

  const patch: S.Schema<Patch> = schema.pipe(
    S.pick("id"),
    S.extend(schema.pipe(S.omit("id"), S.partial())),
  );

  return patch;
};

Type 'extend<SchemaClass<{ id: T["id"]; }, { id: T["id"]; }, never>, SchemaClass<{ [K in keyof Simplify<Omit<T, "id">>]?: Simplify<Omit<T, "id">>[K] | undefined; }, { [K in keyof Simplify<...>]?: Simplify<...>[K] | undefined; }, never>>'
  is not assignable to type
    'Schema<Patch, Patch, never>'.