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Smoke-filled room is used in politics to mean:

a room (as in a hotel) in which a small group of politicians carry on negotiations

• Merriam-Webster

The phrase originated in the U.S. to describe decision making done behind closed doors, cloaked in secrecy, and in the early 20th century, probably clouded in literal tobacco smoke.

Merriam-Webster and other sources point to 1920 as the origin date of the expression. Indeed, early uses of this that I can find phrase appear to be in reference to the 1920 Republican nomination of Warren Harding, but I can't find any text references that actually date back to 1920 or the closely subsequent years.

For example, this clipping refers to "the 'smoke-filled room' nomination of Harding."

The old guard dominated, or nearly dominated, republican conventions from that time on. Its members had much to do with the steam-rolling of Roosevelt in 1912 and the "smoke-filled room" nomination of Harding in 1920.

• 
  1933 - Marshfield News-Herald (Marshfield, Wisconsin) 22 Feb. 3/3 (paywall)

Searching book and newspaper corpora, I found that most references to the phrase "smoke-filled room" in the 1920s were literally discussing fires. In the 1930s, the meaning related to politics seemed to become more prevalent than literal uses.

Question

Given how often this phrase is explained as a reference to the nomination of Harding, are there examples that can be found in print showing that the term itself was used at the time to describe the nomination process, or did "smoke-filled room" come to describe the nomination contemporaneously? And is it possible to tell approximately when was the term generalized to refer to private political meetings unrelated to the Harding nomination?

smoke filled from etymonline.com

Meaning "filled with smoke" and meaning "resembling smoke" are from
late 14c.

A smoke filled room in politics, 1920: Encyclopedia of Chicago

The original smoke filled room was in Chicago's Blackstone Hotel,
where, according to an enduring legend, a small group of powerful
United States senators gathered to arrange the nomination of Warren G.
Harding as Republican candidate for president in 1920.

This the earliest I could find with a definite reference to politics, as you also referenced. As with 'smoke and mirrors' I believe the figurative use came to mean duplicitous political machinations behind the scenes, with or without the smoke.

And from TDF, the idiom:

a smoke-filled room

COMMON If someone says that a political or business decision is made
in a smoke-filled room, they mean that it is made by a small group of
people in a private meeting, rather than in a more democratic or open
way. We're not going to see a return to the smoke-filled room, in
which a few ministers and company bosses made all the decisions. Note:
This was first used to refer to the suite in the Blackstone Hotel in
Chicago where Warren Harding was chosen as the Republican presidential
candidate in 1920.

The phrase smoke-filled room was used to describe a drinking establishment that wasn't well ventilated (and before that, the interior of a building on fire), so the extension to party meetings is pretty straightforward:

1893: At times Maggie told Pete long confidential tales of her former home life, dwelling upon the escapades of the other members of
the family and the difficulties she had to combat in order to obtain a
degree of comfort. He responded in tones of philanthropy. He pressed
her arm with an air of reassuring proprietorship. " Dey was damn jays,
" he said, denouncing the mother and brother. The sound of the music
which, by the efforts of the frowsy- headed leader, drifted to her
ears through the smoke-filled atmosphere, made the girl dream. She
thought of her former Rum Alley environment and turned to regard
Pete's strong protecting fists. She thought of the collar and cuff
manufactory and the eternal moan of the proprietor: " What een hell do
you sink I pie fife dolla a week for? Play? No, py damn. " She
contemplated Pete's man-subduing eyes and noted that wealth and
prosperity was indicated by his clothes.

.

1902: In his smoke-filled, untidy best room Darden sat at table, his drink beside him, his pipe between his fingers, and open before
him a book of jests, propped by a tome of divinity. His wife coming in
from the kitchen, he burrowed in the litter upon the table until he
found an open letter, which he flung toward her. " The Commissary
threatens again, damn him! "

.

1948: I have no particular views on Carlisle: I have never been to Carlisle, and never seen these State-managed houses in operation: Only
one comment I would permit myself on the speech of the hon: Member for
Carlisle (Mr: Grierson): He referred to the large, well-ventilated
rooms found in Carlisle public houses: Many of my constituents, I am
afraid, prefer to do their drinking in small, smoke-filled rooms, and
I have no objection to their doing so, if they wish

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