I'm not an engineer, or propeller designer, just an airplane pilot and owner. It's been said that propeller design is part science and part black art, but here's a few rules and thoughts:
Think of prop pitch like transmission gears. A flatter pitch is like low gear, faster to accelerate and quicker to respond, but with lower top speed and less efficient in cruise. Conversely, a coarser pitch will be less responsive to power input changes and will have a higher top speed. My airplane gets around this problem by having a variable pitch prop, analogous to the transmission in a car. For take off, a flatter pitch is used for faster acceleration, and for cruise,, a coarser pitch for higher top speed and efficiency. Another rule of thumb is that a longer, slower turning prop is more efficient than a shorter, faster turning prop. Higher prop tips speeds generate more noise. As prop tips approach the speed of sound, noise increases dramatically and efficiency drops.
Your drone has limited room and clearance for a longer prop, the tips need to clear the drones structure. The props are designed with flexible blades, to a degree this allows the prop to behave like my airplane's variable pitch prop, but it also means they prop needs more clearance to avoid striking the structure.
Prop pitch and length will also needs to match available motor power. Too much prop (pitch and length) will bog down a lower power motor, yet an undersized prop, or one with too flat a pitch, won't be able to harness and use more power from the motor.
Prop tip vortices detract from efficiency, the swept, thinner tips are designed to help improve efficiency, reduce tip vortices and reduce noise.
For the larger DJI drones, like my
M2P, "Master Air Screw (MAS) makes slightly larger props that eek out a small increase in efficiency - they don't yet make them for the Mini.