So I pumped a 1 kHz square wave into my DTL OR gate and observed the behaviour with my scope!
The square wave is in yellow, and the blue is the output signal.
You can see the output doesn’t drop back to zero quite as fast as the input.
You can see on the multi-meter to the right that the current draw is about 5.83 mA. That’s consistent with my earlier measurements given a duty cycle of 50%.
And you can see in the following photo that the frequency response of the circuit is rubbish. If you go much above about 10 kHz the output just stays “on”.