Left crank has become loose and no longer stays on the bike

Do you need a 10 speed triple? Any more recent replacement of M622 shoud work (Hollowtech II bottom bracket). FC-M6000 should be absolutely fine. You just need to choose a double or a triple, just choose the appropriate variant (M6000-2 vs. M6000-3).

If your rings are still in good condition, it's likely that you can replace just the left crank. https://www.sjscycles.co.uk/cranks-left/ Lists some that are available now. If you have (as your model number implies) a Hollowtech II crankset, any mountain crank using the same system will fit. As the main spindle is quite a hard steel, it doesn't usually get damaged from this type of problem. Remember, you can't look at both sides of the bike at the same time! (unless you use a mirror).

In addition, make sure you are installing the cranks correctly. Hollowtech 2 cranks are very robust and shouldn’t just spontaneously fall off.

• Loosen and tighten the two pinch bolts in very small increments, 1/4 turn max at a time. Make sure to alternate sides.
• It is imperative to use a torque wrench on these two bolts. If the tension is uneven, the crank won’t clamp on properly and is very liable to fall off. If you can’t access a torque wrench, tighten the bolts pretty much as hard as you can go with a regular length Allen key. If the threads strip out, your suspicion was correct: the threads were damaged.
• Use threadlocker on the bolts.