I’m not a betting man. I wish I was. (If I was, I would have made a few quid on those foolish offers from the betting sites.)
When London’s local paper, the Evening Standard, reprinted its 1900 edition for the pseudo-millennium, it had no mention of a new century. And I do remember accounts of celebrations in 1901 - and “what they said last time” reprints in some paper or another which reprinted 1/1/1901 editorials.
I have seen a reprint of a Times of London editorial where the paper stated (in 1899) that the new century, according to the Times, was going to start January 1, 1901 and that was the end of the discussion.
So, people thought about this issue, but it was nowhere near as big a deal as it was for 2000 because of the “Odometer Effect.”