second or third conditional

Since it's a past tense narration

It depends how far into the past and what may have changed since that time.

If the author is writing during the 21st century about something that happened in the 19th century then they might say "the ceremony that would normally have been due". This indicates that such a ceremony may not exist in the present. Of course, if there were tsars in the present, they would be afforded some ceremony but maybe a different ceremony.

If, on the other hand, the author was writing during the 19th century about something that had happened shortly beforehand, they would write, "the ceremony that would normally be due his rank". This is because, at the time of writing, the ceremony would still be appropriate and normal.

Does this answer the question?