No, those affect your character's jump distance. Mighty Leap lets you make a jump of up to 20 feet per psi point; it does not change your jump distance.
From the rules for Jumping:
Long Jump. When you make a long jump, you cover a number of feet up to your Strength score if you move at least 10 feet on foot immediately before the jump. When you make a standing long jump, you can leap only half that distance.
High Jump. When you make a high jump, you leap into the air a number of feet equal to 3 + your Strength modifier (minimum of 0 feet) if you move at least 10 feet on foot immediately before the jump. When you make a standing high jump, you can jump only half that distance.
This is a character's jump distance for High and Long Jumps respectively.
Consider the Jump spell:
The creature's jump distance is tripled until the spell ends.
This multiples your jump distance by 3.
Consider Step of the Wind:
your jump distance is doubled for the turn.
This multiples your jump distance by 2.
Consider Boots of Striding and Springing:
you can jump three times the normal distance
The wording is a little different, but again the "normal distance" is your jump distance, and you can jump 3 times that amount.
Now for Mighty Leap:
Mighty Leap (1–7 psi). As part of your movement, you jump in any direction up to 20 feet per psi point spent.
It does not say that it changes your jump distance. It has no interaction with the above, because it ignores your jump distance completely.
Here are some wordings that would interact with the above:
- When jumping, your jump distance increases by X feet per psi point spent.
- When jumping, your jump distance is Y feet per psi point spent.
- When jumping, you jump an additional Z feet per psi point spent
Unfortunately, Mighty Leap doesn't say anything like that. It just says that you jump 20 feet. You do not make a normal jump with bonuses, and you do not modify your jump distance.
Finally, your example:
For instance, Merry the Mystic uses Mighty Leap with 2 psi points for a 40-foot jump, but is also wearing Boots of Striding and Springing. Assuming Merry has at least 120 feet of movement available, would the boots make him jump 120 feet instead of 40 feet?
Merry only jumps 40 feet. Mighty Leap lets you jump up to 20ft per psi point. It does not increase your jump distance to 20 feet.