While investigating something else, I created a new profile, then signed into sync, expecting my settings to be carried over.

Most were, but it appears my default search engine was not. My default on my main profile was DDG, but when I typed a search, I was taken to google:

Expected result: DDG is search engine after syncing.

Thanks for filing this! We don't sync search engines yet—bug 444284, comment 80 has the gory details.