Calling the RF generator a "Hartley" is a stretch too far to bear.
I hope that stripping this oscillator/modulator to its bare bones, but maintaining its functional operation doesn't cause grief. I'm just too lazy to include every component. For example, biasing uses Thevenin equivalents.
C3(100nf) provides positive feedback causing the two upper transistors to oscillate at the carrier frequency. Q1 varies audio-frequency current to the two upper oscillating transistors. Q1's collector current swings between 0 up to about 28mA at 1kHz here.
The purpose of C4(56pf) and C2(27pf) is unclear.
One might be careful of the oscillating tuned network (L1+L2, C1 and Rload). Without Rload, collector impedance of Q3 becomes so high that Q1 swings into a non-linear region where RF voltage swings below base voltage (near +5V). When Rload becomes high enough, the tuned network Q is reduced to the point where Q3 runs without base-collector forward bias at Q3. The plotted V(n004) monitors the node where Rload meets L1. This node is where the antenna is placed.
The antenna provides the necessary loading to keep Q3 from clipping. With no antenna Rload is small, amplitude becomes too high (light green plot where Rload=5 ohms). The transition point between clipping and proper operation in this simulation is where Rload>10 ohms roughly.
In my opinion, C2, C4, C5 and R3 are not necessary as primary functional parts. Their purpose may be to discourage oscillation at much higher frequency than desired... it is possible that this circuit could oscillate at 10's or 100's of MHz otherwise.