That doesn't make sense. You use AWS services because they are in the cloud, not because you want to do self-hosting. Similar to Cloudflare wrangler, localstack should be just a well-built local mocking service.
If you're a cost-conscious startup, you could use AWS Local Thingie to run it on a 5€/month VPS while you validate your idea.
Then if you get actual customers you could move it to proper AWS - or you might find out that Fake-AWS is actually enough for you and a 20€ VPS is enough for your uses and pay 0€ to Amazon, while still filing bug tickets to AWS Local Thingie Github for bugs and feature requests =)