„I’m new to cello, so maybe it is a silly question, but is it normal to have slightly dark fingers after playing?”
Don’t be afraid, it is normal. Most strings, especially new ones, can turn your fingers grey as the metal winding rubs off while you’re playing. It will lessen after the strings are used for a bit.
Sometimes it can be caused by less expensive ebony fingerboard that is dyed. It happens especially in cheap cellos.