But software programmers don't qualify for TN visa. System analyst is the closes I think.
They do under either Engineer or Computer Systems Analyst, depending on the case.
They do if they have a Software (or otherwise) Engineering degree, and getting in as a CSA just means you need to have 'microservices' and 'managerial' duties in your role
Wrong. You just need to phrase it the right way. The government bureaucracy considers programmers as typists, and systems analysts as programmers.
And if the border guard doesn't like the wording, they'll reject you at the border.