I'm the product manager at Medium who manages the Boost Nomination Pilot, and I can say that no, there are not Mini Boosts. Boosting is a binary function: the story either is or is not Boosted.

It sounds like your story last year just organically found readers! Boosting is just one way stories get distributed across the platform and every month there are thousands of stories that reach large audiences that are not Boosted.

More about all this over here:

https://help.medium.com/hc/en-us/articles/360018677974-What-happens-to-your-post-when-you-publish-on-Medium