SST refresh exits with `1` while Pulumi exits with `255` newly created APIGW + Lambda resource

[fabryscript]

Repro:

• Have an already deployed SST APIGateway resource
• Add a simple route
• Run sst refresh --verbose --print-logs

Pulumi will exit with error code 255 and with the following log:
✓ Refreshed
Router: https://***.cloudfront.net
Api: https://***.execute-api.eu-west-1.amazonaws.com
---
api: https://***.execute-api.eu-west-1.amazonaws.com
router: https://***.cloudfront.net

time=2026-04-10T19:53:35.758+02:00 level=INFO msg="INFO unlocking app=aws-bun-test stage=fabryscript"
time=2026-04-10T19:53:35.973+02:00 level=INFO msg="shutting down server" service=server
time=2026-04-10T19:53:35.973+02:00 level=INFO msg="server done" service=server
time=2026-04-10T19:53:35.974+02:00 level=ERROR msg="exited with error" err="stack run had errors"

The state gets refreshed, but pulumi will still error.

Previous lines show:
time=2026-04-10T19:53:31.499+02:00 level=INFO msg="rpc request" method=POST url=/rpc
time=2026-04-10T19:53:33.860+02:00 level=INFO msg="rpc request" method=POST url=/rpc
time=2026-04-10T19:53:33.863+02:00 level=INFO msg="rpc request" method=POST url=/rpc
time=2026-04-10T19:53:34.022+02:00 level=INFO msg="INFO pushing partial state updateID=[redacted]"
time=2026-04-10T19:53:34.606+02:00 level=INFO msg="pulumi exited" service=project.run updateID=[redacted] err="exit status 255"

SST Version: 4.5.0

Minimal example code to repro:

/// <reference path="./.sst/platform/config.d.ts" />

export default $config({
	app(input) {
		return {
			name: "aws-bun-test",
			removal: input?.stage === "production" ? "retain" : "remove",
			protect: ["production"].includes(input?.stage),
			home: "aws",
			providers: {
				aws: "7.23.0",
			},
		};
	},
	async run() {
		const router = new sst.aws.Router("Router");
		const api = new sst.aws.ApiGatewayV2("Api");

                 // Remove this, then run refresh -> deploy, it will run just fine
                 // But after adding this, and refreshing, pulumi will exit with 255 and sst with code 1
		api.route("GET /a", "functions/a.handler");

		return {
			router: router.url,
			api: api.url,
		};
	},
});