I want to fly from CTG to BOG to connect to a LH F award to FRA/ARN on a separate ticket.

It is significantly cheaper to book a “hidden city” flight, but then I would obviously not be able to have my bag checked all the way through.
But is it likely they’d check my bag through to FRA/ARN if I buy just the CTG-BOG flight?

Prices are like this:
CTG-BOG-MDE economy 150$
CTG-BOG-MDE business 220$
CTG-BOG economy 230$
CTG-BOG business 270$

Prices are per person, we would be 2 pax traveling, so effectively all prices are x2...

Which option would you book?