In the 1928 Scribner’s (NY) edition of The Plays of J. M. Barrie, I’ve noticed an odd convention: where a contraction happens in middle of a word (e.g., “don’t” for “do n(o)t”), the apostrophe has the usual appearance. But when the contraction removes the entire first part of the word (e.g., “it’s” for “it (i)s” or “I’ll” for “I (wi)ll”), the typesetters consistently left the inter-word space there: not “it’s” or “I’ll” but “it␣’s” or “I␣’ll”:
Was this standard usage a century ago, either in the U.S. or in Britain?
No. The vast majority of books of the period that don't follow that convention.
Is this the sort of authorial quirk (like the use of “sha’n’t” in Winnie the Pooh) which should be preserved in a reprinting?
Apparently not. Some writers have had general opinions on apostrophes that were either unusual or old-fashioned for their time (Lewis Carroll's and A A Milne's sha'n't vs George Bernard Shaw's shant *) and some broke from standard use for particular purposes (Joyce's Finnegans Wake and E E Cummings' "Buffalo Bill 's") but I haven't found anything to suggest that Barrie was unorthodox in this matter.
As a rule, the final decision on such matters lies with the editor or (historically) the printer. This remains true today, though modern digital formats mean that an editor might today decide to do minimal work on the document received in their email while in the past it would have been necessary to produce printing instructions from either a hand-written manuscript where spacing would be more arbitrary or from a type-written typescript where spacing would be limited by the technical limitations of typewriters.
While editors might defer to authors' wishes with greater or lesser amounts of screaming and hair-pulling involved (or to what they believe to be their wishes in the case of E E Cummings who many are still convinced liked to be called e e cummings), most of the time most writers are either happy enough if the result is something one could reasonably call "normal English punctuation" or else are consciously so far away from the norm that the editor has no choice but to follow them. Sometimes the author may not even know that a new edition is being prepared (not least if they aren't alive any more).
So our starting point would be to assume that this was a style decision by the publisher, not the author, unless we've a reason to suspect otherwise.
We can find further evidence of this edition of Edith Wharton's Sanctuary by the same publisher where we've an example of similar style used with would n’t and had n’t:
So, this seems to be a matter of Charles Scribner's Sons' style rather than of Barrie's.
Now, Hot Licks' turn of phrase in a comment on the question raises an interesting point:
…that bastion of linguistic propriety "The New Yorker"…
The truth is, The New Yorker is not, and never has been, a bastion of linguistic propriety when it comes to punctuation: They chose a policy on punctuation matters that was unusual, but defensible, at the time, and then they stuck with it even as the rest of the world became firmer in doing something else. The same applies to some of their spellings and spelling out of large numbers.
If we were to call something "linguistic propriety" it would mean insisting on something more "proper" than others. Some people might like the New Yorker's style (hey, I love me some diæreses) but one would need a particularly pig-headed sort of pedantry to not only insist that there was one true rule on whether reëlect has a diæresis or not, but that this one true rule said that it did, in the face of it being the more unusual spelling. Even the sort of person who spells the word diæresis isn't likely to claim that.
So, let us take the New Yorker as a data-point, showing that in 1925 there was a magazine that took an unusual stance on spelling and punctuation (they were as much against the hyphen in re-elect as they were in favour of the diæresis in reëlect) despite it not being the approach followed by the house styles of pretty much anyone else.
At the same time, let's consider that the exact way in which the apostrophe is used has changed over the course of its use in English.
Let us also consider that a regular driver in people's house styles is a wish to be logical. We can see what the typesetter was getting at with their it ’s in using the apostrophe to mark an elided i but not an elided space.
Let us also consider that punctuation generally has changed in printed English. The spacing around quotation marks, colons, semi-colons, question marks and exclamation marks have all changed in terms of what is normal, with the eighteenth century once favouring the likes of “ What should I ask ? ” rather than “What should I ask?”. At some point we were brought from that norm to our current norm by people who at the time were mavericks.
And let us finally consider that there are still matters where style-guides disagree with each other, along with idiosyncrasies that persist.
And with all that in mind, it seems likely that what we have here is a style in use in a particular publishing house, arrived at by the argument that it retains something of the pre-contracted words that other styles do not, which did not catch on, but which was a conscious style: If it was a blunder, someone would have pointed it out between the 1903 edition of Wharton I found and the 1928 edition of Barrie you found.
That said, their reasoning is not sound; it ’s does not do a good job of giving written form to the word it’s, because it suggests it's pronounced as two syllables.
*And indeed A A Milne's accounts of his young niece's writing style, though we should probably take his explanation that she was emulating Shaw in this regard with a pinch of salt.