Hello.

manfed
Beta is assumed, because in "serial" production no one will select transistors, even in a given group of reinforcements. The Worst Circumstances Method is always used in projects. Secondly, you measure beta "at a given current", which does not mean that it is the same for 1 mA and 10 mA. The catalogs give the measurement conditions with the hfe table.
Saturation conditions refer to the load current. Catalogs give average or max values.
Assuming you have full 5V at the output then
Ib = 5V - 0.7V / 2.3k = 1.87mA
for beta = 50, the maximum collector current can be 93mA. If it is larger, the transistor will not be saturated and the difference Uce > 0.2V.
If we want to reduce the load on the source (LPT in this case), we use darlington transistors. They have a very large beta, which is the product of the gains of the component transistors.
If you connect a load between the emitter and ground (for an NPN transistor), the load current will "raise" the potential of the emitter relative to ground, which will cause the transistor to clog and establish new equilibrium conditions (I assume constant base drive). The supply voltage will be divided into Uo and Uce.
Previously (for R = 2.3k), there was probably an overload of the port and the output voltage was lower, which consequently reduced the base current.
The working circuit of the transistor is a common emitter. Analyzing from the voltage side, it is an inverter.
greetings