Hysteresis threshold changed when connecting a transistor to the output of a comparator LM393,
You made R5 (200 ohms) too low.

The LM393 has an open collector output which can only pull the output low. So that's why R4 is needed. R4 is the only component pulling the output of the LM393 high.

Now imagine that the LM393 does not pull the output low, then its output is open, it cannot pull the voltage up (since it is an open collector of an NPN transistor). There's only R4 pulling the voltage up.

You're also loading the output of the LM393 with R5 (200 ohms) and an NPN Base-Emitter junction. There will be around 0.7 V across that Base-Emitter junction. That 200 ohm will not drop much voltage so the LM393's output will be slightly above 0.7 V, maybe it will reach 1 V.

For the hysteresis levels you calculated the LM393's output must be 5 V (supply voltage). This will not happen until you increase the value of R5.

Also you do not need such a low base resistor for Q1 as Q1 has plenty of current gain. Increase R5 to around 4.7 kohm, that will still not give you the right upper threshold level but will be much closer. You might also need to lower R4 to 1 kohm and then you should be quite close.

A simpler solution was suggested by Trevor: throw out R4 and Q1 and replace these with an NMOS.

If you don't like NMOSFETs you could add a 2nd NPN to make a Darlington type configuration:





This makes the current through R5 so small that it barely influences the levels at V1.