The situation:
After upgrading the CDK CLI package with npm, every CDK command in the app failed with Cloud assembly schema version mismatch: Maximum schema version supported is 10.0.0, but found 11.0.0, plus This CDK CLI is not compatible with the CDK library used by your application. The CLI and library versions looked compatible on paper. The root cause was a bug in npm version 7 itself, which broke the CLI install; npm 6 and below were unaffected.
What actually fixes it (verified in the thread):
This is caused by a bug in npm version 7 (npm/cli#3196) corrupting the aws-cdk CLI install, not by a real version mismatch. Reinstall the CLI using npm 6, or upgrade npm past the buggy 7.x range, then reinstall aws-cdk fresh. After a clean install with a working npm, the CLI and library schema versions line up again. The same class of error can also appear when the global CLI genuinely lags the library, so make sure the global aws-cdk is at the latest too.