Something is pretty loose if you feel movement while pedaling.

Have you tried:

- Moving the cranks forward and back against each other by hand? This would show loose crank- quite common.
- Spinning the crank by hand with chain removed? Rough or play shows worn or loose bottom bracket.
- Checking chainrings for damage or loose bolts?
- Checking the pedals are installed tightly & bearings are smooth?

If the crank is loose, it cannot be simply tightened.

Apologies if you've already addressed this stuff.