I looked into this locally. What it says on the tin, "Error: Could not find module @ember/application/deprecations imported from @ember/string/index", is of course, correct: The included version of @ember/string references @ember/application/deprecations. The @ember/string dependency seems to come from ember-data.
So we need a release of @ember/string and it looks like that will have to be a major bump because of dropping node versions.
and then we'll need a new ember-data beta, updating the dep on @ember/string

Updated ember-data with the updated @ember/string. Still failing under Embroider with

Uncaught TypeError: Cannot read property 'String' of undefined at webpack://some-cool-app/../node-bDXlVehj.tmp/node_modules/ember-inflector/make-configurable.js?, line 1

Looks to be the same errors as in #9597

Updating embroider seems to have made the build failures multiply.

OK reverting that last commit