A sawtooth oscillator breaks down at higher frequencies
This design depends on constant-current from Q1, and its GBW and \$beta\$.
If this is real hardware you seriously need a bypass capacitor of 100 nF and 100 uF across 5 volts to ground. This is what helps make HF designs stable.
Replace R1 with 2 1N4148 diodes in series to lock the voltage of R3 at ~650 millivolts. Reduce R2 so bias current for diodes and Q1 is ample. R2 can be as low as 2.2 K without heating the diodes or Q1.
Still, R3 will have a low limit based on the gain of Q1. A super-beta transistor might give you more range for high and low current for the ramp.
I assume that the 5 volt supply is very stable. If not R2 should be a 2 mA current sink.
I understand your pushing boundaries here, so you will always find upper and lower limits, however the right type for Q1 plus the diodes might get you to 1 MHZ.
Scour the datasheets to find a Q1 with a GBW of 100 MHZ, as full power frequency is a tiny fraction of this value.
@jonk is offering better designs of more-or-less the same circuit. If you want something better (but not laboratory grade), listen to what he says.

EDIT: A 10 uH tiny inductor in series with the diodes would create a lot of instability, or replace 1 diode with a 620 ohm resistor. Out of many sawtooth generator schematics, you picked the most minimal design, so it will be the most finicky. Due to lack of self-oscillating parts and feedback, it seems to work by accident, depending on abstract bjt properties.