Support for Server-SentEvents (SSE)

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**Tell us about your request**

Perhaps this is related to https://github.com/aws/apprunner-roadmap/issues/13 but it doesn't seems as though SSE events are supported yet?

I've deployed a simple application but at the moment the server attempts to send a message to the browser it triggers a `The connection to https://{APPNAME}.awsapprunner.com/sse/ was interrupted while the page was loading.` error.

**Describe alternatives you've considered**

Uncertain. I'd really like to be able to use SSE messages with App Runner applications but maybe just falling back to a plain-vanilla EC2 + ALB setup.

No repository files, tests, or implementation entry points are mentioned. Start by reviewing AWS App Runner's current SSE support and the related issue linked in the report; done means App Runner applications can maintain SSE connections without the reported interruption.

Written by the indexing model from the issue text.