Connecting PWM computer fan to transistor and adjustable resistor
What you show will be basically 'all on' or 'all off'. It won't properly regulate the fan speed. Even if you were able to make it work, it would be hugely inefficient. (It could be made to work using a current mirror technique, but this would destroy that poor 2n3904 in short order.)
You've probably seen circuits like that using an NPN or a FET on the low side. It's the common way to control a 2-wire fan (or for that matter, any DC motor) very cheaply. What you're missing is that these circuits use a PWM signal to control the transistor, essentially 'chopping' the current to reduce the power delivered to the fan. These work without killing the transistor because the transistor is either fully-on (saturated) or fully off, so it isn't shedding much power.
Whether PWM-chopping the power works or not depends on how tolerant the brushless DC (BLDC) fan motor is of having a chopped voltage: some are ok with it, some fail.
Fortunately, you have a solution literally in-hand. Intel, in their infinite wisdom, specified that their standard platforms use a 4-wire-fan, which includes a separate PWM input. This input chops the coil driver voltage, but keeps the BLDC controller powered up, so it works perfectly over a wide range of PWM frequencies and duty cycles.
Lucky for the rest of us not making PCs, Intel's benevolence ensures a cheap and available supply of these easy-to-use 4-wire fans.
You've got a 4-wire PWM fan. Awesome, you're one step ahead of the game. So make a PWM signal and drive the fan's PWM input. This takes advantage of the fan's built-in chopping circuit to regulate the fan speed, giving you full control from 0 to 100% fan speed.
You can make a PWM signal with the venerable 555 timer IC. Here's an example: https://www.electroschematics.com/pulse-generator-with-555/
And another: https://colourtvservicebbsr.blogspot.com/2016/04/pwm-speed-motor-controller-by-ic-555.html
The chop frequency for PC fans is normally 25KHz, but you can use lower frequencies (like 100-300 Hz) if you wish if you don't mind about hearing the 'chop' noise from the fan.
Later, you could enhance your design using an R/C proportional control, which uses PWM to control servos.