I just flew Condor J from Seattle to Frankfurt. If you have TSA precheck, you have to go to the check in counter to get a printed boarding pass with the PreCheck logo. While at the desk, the agent did have me weigh my rolling carry-on (gave me a little "approved in cabin tag), but didn't address my backpack (although it is not a large size) nor my crossbody purse (also smallish). My Frankfurt flight was on Lufthansa EuroBiz and no one batted an eyelash at my carry-ons. If you are in an early boarding group, you'll probably be fine, otherwise you may gate check so bring some AirTags.

I actually connected in Frankfurt on a separate ticket (self-transited) but love their transit process there. Doesn't take 1+ hours like LHR and CDG. Refreshing.