Electronic – How to U_CE be smaller than U_BE in this circuit

I think you'll probably find your answer in the L293 data sheet - it's the lower-power version of the 298 (without the heatsink). Here's what the 293 output stage looks like: -

The 293 (and I strongly suspect the same for the 298) has a PNP transistor that is much more conveniently driven from a low side logic signal.

I'm fairly sure the two devices work internally the same way - they have pretty-much exactly the same poor output specification. The diagram shown in the 298 spec "hints" at the limitations inherent in this type of H bridge because of the use of NPN transistors at the "top" and darlington transistors at the "bottom". See also this for alternative devices using MOSFETs.

You will be fine with BC548, BC547 or 2N3904 your application is not demanding.

The history of this comes from the original metal can NPN silicon devices that were called BC107, BC108 and BC109. These numbers are in ascending gain and descending breakdown voltage. According to semiconductor physics gain and breakdown voltage are interchangeable. High voltage transistors tend to have lower gain and low voltage transistors tend to have higher gain. The gain differences are not huge when comparing the 547 & 548. Early analogue circuits that had no negative feedback using the minimum number of BJTs were much more gain sensitive and ran on 9V so the BC109 with its h_fe of 900 was sought after. According to folklore the manufacturer put the numbers on the transistors after they were automatically tested. Packaged transistors that didn't make the specification in one or more aspects were sold to hobbyists as F PACK's and they were big cheap bags.