Correct. You can see exactly how we're constructing the messages here: https://source.chromium.org/chromium/chromium/src/+/main:ser...

Note that in addition to normal HPKE we're also adding a Date header to the encrypted headers and padding the contents.

Correct me if I'm wrong, but either the user encryption key is unique and hence the user is identifiable to Google, or a finite number of keys is used which makes the encrypted text subject to identification because a finite number of inputs can produce a given output.

My cryptography education is rather superficial, so I might be missing something.