NMOSFET not turning off properly using RPi GPIO pins

The reason the FET turns off so slowly is because you only have 2 kΩ pulling it high. Take a look at the datasheet for that FET. It should show you the actual and effective gate capacitance when switching. The relatively weak 2 kΩ pullup is working against that capacitance.

Here is a trick I sometimes use in this situation:

The double emitter follower is basically a impedance buffer. The current to charge and discharge the gate capacitance is handled by Q1 and Q2, so the signal at GATE can be much higher impedance and still switch the FET quickly. Note that this double emitter follower will loose 700 mV or so on each end. That is fine for a FET that switches over a 10 V gate range. It will still be "off" with 700 mV on the gate just as well as with 0. At the other end, its usually easy enough to drive GATE the extra 700 mV further than what you want to make sure shows up on the gate of Q3.

You can easily increase the gate voltage by 1.2 .. 1.4 V using a pull-up resistor and a couple of diodes:

This will toggle gate voltage between 1.2 and 4.5V instead of 0 and 3.3V. There may be a small current flowing into the PIR when it drives its output high, which is undesired but which the PIR will most probably cope with.

A more elaborate solution using an extra BJT would be:

^{simulate this circuit – Schematic created using CircuitLab}

This will drive the gate between 0 and 5V, as you did manually, so it should work.