Gutenberg disables the global block inserter when code editing is on:

Since we override that inserter with our custom one, that doesn't work in the Stories editor.

We should align behavior here so that the inserter is disabled as well.

Also, the shortcuts in the toolbar should be disabled and the current block should be de-selected.

Gutenberg's behavior is documented in an e2e test:

https://github.com/WordPress/gutenberg/blob/2f757fa8012edb5cd684a26adef9cb4e8c2158db/packages/e2e-tests/specs/editor-modes.test.js#L88-L118