auth.api.signInAnonymous doesn't set session cookie.

import { initTRPC, TRPCError } from "@trpc/server";
import type { Context } from "./context";
import { auth } from "./auth";
export const t = initTRPC.context<Context>().create();

export const authenticationOrAnonymousProcedure = t.procedure.use(
  async ({ ctx, next }) => {
    let session = ctx.session;
    if (!session) {
      const anon = await auth.api.signInAnonymous({
        headers: ctx.headers,
        returnHeaders: true,
      });
      session = await auth.api.getSession({
        headers: anon.headers, // Tried ctx.headers and didn't work either.
      });
    }
    return next({
      ctx: {
        ...ctx,
        headers: ctx.headers,
        session: session!,
      },
    });
  }
);