When was the phrase "smoke-filled room" first used in politics?

The 'smoke-filled room' of US politics, wherein the will of the people and so democracy itself is subverted by the machinations of unelected power brokers in private negotiations, became an emblem of that process after Harry Daugherty, Warren G. Harding's political manager during the build-up to the latter's successful 1920 US presidential run, made a prediction that the Republican nomination would be decided in such a room. According to Leonard Wood, who would later be Harding's chief competitor for the 1920 Republican presidential nomination, as quoted in an article datelined "Special to the New York Times", "Cleveland, Ohio, April 1" (The New York Times 02 Apr 1920, emphasis mine, paywalled),

The favorite son plan has been one which has always placed a limitation upon the choice of the people and has played directly into the hands of the worst form of machine politics. It has resulted often in bringing about in the States what a distinguished political leader recently said in Washington would be done in the 1920 Presidential nomination, namely, that about 2:11 A. M. the nomination would be settled by fifteen or twenty tired men sitting around a table in a smoke-filled room behind locked doors. We want no more of this in this country. We want the will of the people as expressed at the polls embodied in the choice made at the convention. When the time comes that fifteen or twenty men can gather in a smoke-filled room and settle the Presidency, may God pity us! No one else will.

Although Daugherty was not named in that article, nor in any of the subsequent versions of it I could find printed prior to the 8-12 June 1920 Republican convention (for example, 11 Apr 1920, The Lincoln Star, Lincoln, Nebraska [paywalled]; 16 Apr 1920, The Alliance Herald, Alliance, Nebraska [not paywalled]), an article in the 15 June 1920 Virginia Chronicle (Roanoke, Virginia; not paywalled), datelined "Chicago, June 14", makes the connection explicit:

Harry Daugherty made a mistake. Three months ago as campaign manager for Warren G. Harding, he predicted that about 2:11 a. m. "in a smoke-filled room" on a certain night during the Republican national convention, the next nominee would be chosen. His mistake was on the time — it was 3:11 a. m.

Before Daugherty's self-aggrandizing and, to an extent, self-fulfilling prediction, the 'smoke-filled' room had been an emblem in search of an attachment. Apart from uses referring to structure fires, the phrase appeared in political, judicial (as a description of the jury room), and other contexts. Two of those uses from 1919 merit quoting at length:

Senator Reed, alleged democrat, of Missouri, seemed to be very proud of the fact that he helped the republicans and Senator Gore in killing the peace treaty. The Washington correspondent of the New York Evening Post, after giving a vivid description of the scene in the senate when the final fight was made over the peace treaty — the jesting of the republicans and the solemnity of the democrats, battling for peace in the hazy atmosphere of the smoke-filled room — draws a final word picture of the climax, with "Senator Jim Reed standing in the center of the floor with Reed's arm resting on Lodge's shoulder." What a fine picture this would make to adorn the homes of admiring Huns!

The Daily Oklahoman (Oklahoma City, Oklahoma) 30 Nov 1919, paywalled.

At dawn thousands of citizens had emerged from hotels and lodging houses or walked in from residential districts, while haggard city, federal and strike representatives came from smoke-filled rooms after an all-night vigil.

Lebanon Daily News (Lebanon, Pennsylvania) 08 Feb 1919, paywalled.

Similar uses appear sporadically in the popular news from at least as early as 1911.

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.

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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! "

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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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