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+1'd for your answer, thank you. I'm leaving this open for a bit -- still hoping for something more complete (this answer missed dbDelta, curious if there's other functions/systems to help with migration like tasks)
@TomJNowell Not contesting the close, as you're the moderator and its your calls that define these things for a StackExchange site — but based on my experience in other StackExchange communities I'd argue that a vendor (Automattic) provided solution, or tooling that's so heavily used/ubiquitous that it's a de-facto standard are "canonical enough" and an answer thread that lists these tools still makes the internet a better place (the original "criteria 0" for Stack Overflow answers/questions). If the close-by-default policy ever comes up for review, please consider the above. Best wishes!
"unable to connect to database" is pretty vague -- a description of "I did X, and Y happened" that included specific error messages may help someone troubleshoot your issue.