I assume you tried contacting Lowes customer service.
How about Kobalt:
https://www.kobalttools.com/contact-us
My experience has been that cordless tool parts - especially for discontinued or short-run models are as scarce as hens teeth.
Did your instruction manual even come with a parts diagram? How about some indication of how to get the tool serviced?
I see that one reviewer on the Lowes website had a gear problem too:
https://www.lowes.com/pd/Kobalt-20-Volt-Variable-Speed-Cordless-Reciprocating-Saw-Bare-Tool/50037170
Sadly at one time most corded power tools could be serviced ad-infinitum (sort of like those 1950’;s US cars that they keep running in Cuba) or at least it seemed that way. Over my working life - I had hundreds of tools professionally serviced and did a batch of servicing myself on my personal collection. When the switchover to cordless came in - slowly I started noticing that quite a number tools were being junked and replaced rather than repaired. Not always was it because of changes in battery platform. I recall quite a number of cordless tools (some new corded ones too) that had failed being declared “unserviceable” or “not worth servicing”. I might add that we were not buying house-brand tools - but rather top-of-the-line so called professional grade ones. Maybe this is just another example of planned obsolescence - and for us it was just another cost of doing business and lesson-learned.
Notwithstanding the pessimism my comments may convey - I hope you have good luck with Lowes/Kobalt
Just a stab in the dark but I believe Kobalt is OEM’ed by Chevron. “If” you can find a similar saw of another brand they make you might have some luck… I agree with @fred your basically looking for a needle in a global haystack… sadly.
At $63 for a new replacement tool from Lowes, it almost seems to be a throw away item and not worth the cost or time to rebuild. Last tool I replaced a switch in cost me close to forty dollars for the part plus shipping, not to mention my time spent researching parts and then fixing it when the switch arrived. I think I would shove the current broken tool in a box for possible future parts and bite the bullet on the newer model.