Cannot run Amplify on Localstack

I followed the instructions here: https://docs.localstack.cloud/user-guide/aws/amplify/

Running localstack at 3.2.0. Amplify is 12.10.1.

When I run amplify init --use-localstack true, it seems to work, however this shows up in the localstack logs:

2024-03-17T22:20:02.415  INFO --- [   asgi_gw_1] localstack.request.aws     : AWS amplify.ListApps => 200
2024-03-17T22:20:02.428  INFO --- [   asgi_gw_0] localstack.request.aws     : AWS amplify.CreateApp => 200
2024-03-17T22:20:02.477  INFO --- [   asgi_gw_1] localstack.request.aws     : AWS amplify.GetBackendEnvironment => 404 (NotFoundException)
2024-03-17T22:20:02.536  WARN --- [   asgi_gw_0] l.aws.protocol.serializer  : Response object BackendEnvironment contains a member which is not specified: appId

When I run amplify push --use-localstack true, I get:

✖ There was an error pulling the backend environment dev.
🛑 Stack with id amplify-amptest-dev-162002 does not exist

Learn more at: https://docs.amplify.aws/cli/project/troubleshooting/

Session Identifier: d93cd4a7-0772-4e7d-bfd7-5c04a4740e87

Start with the Amplify LocalStack instructions linked in the issue and reproduce the commands with LocalStack 3.2.0 and Amplify 12.10.1. Compare the logs from amplify init --use-localstack true with the failure from amplify push --use-localstack true, focusing on the missing backend environment and reported stack. Done means initialization and push complete without the missing-stack error or serializer warning.