An amateur historian has discovered a long-lost short story by Bram Stoker

How would copyright law apply here? Would this fall into the public domain immediately? I read that Irish law is that it would be "70 years from date first made available to the public". Since published in a newspaper, I would assume this would be public domain now. Correct?

Yes, it's public domain

If this was an unpublished manuscript, rights of first publication would apply and it might be covered by a kind of copyright that would vary depending on the country. Since this was "rediscovered" after first being unambiguously published back in the 1890s, it's pretty clearly in the public domain.

OP got incredibly lucky though that the author's name was included in the original publication - things like this (i.e. contributions to newspapers or magazines) were often published under obscure pseudonyms, initials, puzzling hints like "By the author of Such-and-such" or no author indication at all.

I _think_ UK copyright law would matter here, since at the time the story was published (1890) the Ireland was part of the UK (Ireland gained independence in 1921.)

If UK copyright applied, then the story would have entered public domain in 1932. The term of copyright for published works at the time as 7 years after the authors death, or 42 years, whichever was longer.

Funnily enough there was a reddit post from around the time the manuscript was discovered (but before it was announced) asking a similar question