IGT stands for "ignition trigger".
IGF stands for "ignition feedback".
The little block on the IGF line is likely to be voltage scaling and overvoltage protection, perhaps an active buffer.
The block on the IGT line is the same, including a driver stage. Those bits are implemented on the IC in the middle of the hybrid.
Why does this circuit need two voltage sources?
It doesn't really. ECU provides properly timed ignition pulses. The W-R line provides 12V when ignition is turned on. The driver inside the igniter needs the 12V supply and the ECU pulses to drive the transistor Tr2 properly. There's only one supply source for Tr2 driver: ignition voltage from W-R circuit. There's only one source of ignition timing pulses: W (IGT) line from ECU.
I don’t understand why TR2 has two voltage sources going to its base.
There is only one signal going to the base. The block it comes out of has a few more transistors that shape the pulses from the ECU and amplify them, and perhaps also protects the coil from a "stuck ON" condition should the ECU get disconnected or fail.
I have considered that the boxes on the right side of the igniter on IGT and IGF lines could be voltage regulators
They are not really voltage regulators, but they are signal conditioning.
If you'd connect B-R directly to ECU's IGF terminal, the ECU inputs would be destroyed probably.
The ECU also doesn't have enough drive strength to control the coil grounding transistor Tr2 - and its output is 5V open-emitter through a protection series resistor. One or two more transistors are needed to develop enough current and the waveform shape needed for coil grounding. Those are in the IC in the center of the hybrid substrate.