chemical launch, on starship in full expenditure mode(500000lbs+payload],ion thrust, solar sail, "accelerator module" that sacrifices itself in an aero braking manouver to then release an in system observation ship
If you can also make the probe survive a close flyby by the star (that should ideally require just a good sun shield & robust orientation control) you could the so called solar Oberth manuever - basically this[0] but to slow down an incoming interstellar probe, not to launch one. A simple storable high thrust solid rocket motor would be ideal for this.
