How Should I Secure My Heatsink for My AM5 Build?

Bent pins typically aren’t caused by a cooler being installed too tightly, unless you really crank down on it, which I doubt you did. It's possible the pins got damaged when you installed the CPU or even beforehand. Those pins are delicate, so I recommend keeping the socket covered as much as possible to avoid accidental contact. As for installation, check the manual for your cooler as each has its own requirements. Watching a few installation videos can also be really helpful.

You really shouldn't need to crank the screws down hard. Gently tighten them while ensuring everything is evenly pressed down. Use an X pattern for tightening, and take care during the CPU placement to avoid putting it in at an angle. That’s a common mistake which can lead to bending pins.

The tightness really depends on the cooler model—some need to be just snug, while others can be tightened more firmly without causing issues. It sounds like your pins may have been bent during CPU installation rather than from the heatsink. Always make sure to insert the CPU straight into the socket; dropping it at an angle can lead to problems.
You should also avoid cranking down on the cooler screws. Tighten them in an X pattern for even pressure—this can prevent unnecessary damage and ensure proper contact with the CPU.