Here are a few potential solutions to achieve variable control of a solenoid actuator:
Pulse-Width Modulation (PWM) Control:

PWM is commonly used to control the speed of actuators, including solenoids, by varying the duty cycle of the voltage sent to the solenoid. This allows for gradual control of the solenoid's actuation by controlling the amount of time the solenoid is energized.
By adjusting the PWM duty cycle, you can control the force and speed of the solenoid's movement. The longer the solenoid is energized (higher duty cycle), the stronger the force, and the shorter the energizing time (lower duty cycle), the slower and weaker the actuation.
Limitation: PWM might still be somewhat coarse compared to a fully linear actuator but can provide more control than a simple ON/OFF approach.
Linear Solenoids with Adjustable Stroke or Force:

Look for linear solenoids that are specifically designed for variable control, such as voice coil actuators. These provide more control over both position and force. Voice coil actuators work similarly to solenoids but allow for smoother, variable control of position, and can be controlled by varying the current sent to the coil.
Some of these actuators can function like linear servos, where the position and speed of the actuator can be finely controlled using a controller.
Electromagnetic Actuators with Feedback:

For more precise control, you could use a feedback system such as a Hall effect sensor to detect the position of the solenoid or an actuator, and use that feedback to adjust the current being supplied.
By combining feedback with a PID controller (Proportional, Integral, Derivative), you can control the position and speed of the actuator more smoothly, almost like you would with a servo motor.
Using a Solenoid with a Spring (for Soft Stop Control):

If you're trying to create a soft stop mechanism for your robotic hand, a solenoid could be combined with a spring or other mechanical system that can absorb excess force or allow the actuator to slow down gradually, which could mitigate the "bear trap" effect you're worried about.
Electropermanent Magnets:

While not exactly a traditional solenoid, electropermanent magnets are a type of magnet that can hold an object in place using a small, low-power current and can be switched between ON/OFF states. This could give you a middle ground where you can control the grip strength in a way that's similar to solenoids but with a more precise holding force.
Conclusion:
For controlling robotic fingers, PWM-controlled solenoids combined with some form of feedback system (like position sensors) might offer a good solution. Alternatively, you could explore voice coil actuators or electromagnetic actuators with integrated control options, as they provide smoother, more precise control over movement.