Of American-English origin, the informal phrase to shoot the breeze means: to converse idly, to gossip; to talk nonsense or to exaggerate the truth.

This phrase occurs, for example, in Sunak and Biden’s bilat falls flat as duty briefly calls in Northern Ireland, by the parliamentary sketch writer John Crace, published in The Guardian (London and Manchester, England) of Wednesday 12^th April 2023:

Well, what was it exactly? Rishi Sunak had been adamant that his morning meeting with Joe Biden was a proper bilat. A wide-ranging discussion with full diplomatic status. The US side? Not so much. They saw it as a quick cup of coffee. Two world leaders who happened to be in the same city at the same time with half an hour to spare. A chance for a quick catchup and to shoot the breeze.

The earliest occurrences of the phrase to shoot the breeze that I have found are as follows, in chronological order:

1-: From the St. Louis Post-Dispatch (St. Louis, Missouri, USA) of Thursday 23^rd December 1909—this text is obscure:

To the Editor of the Post-Dispatch.
I am not a retired banker, but I think Page boulevard man must be a “rummy,” or he was rummy at the time. If he wasn’t rummy he is sure a “gippo,” and the druggist helped him along with a little dope. When he comes back in the evening, druggist shoots the breeze about his four “gippo” sees it plain and digs down and gives druggist four more “bucks” to get five out of soak and then moops away three “bucks to the bad. I don’t see how druggist could be to the bad unless the “Bulls” got next. Come across with the shoes.
VAL.

2-: From the column What Other People Think About You, by Billy Murphy, published in The St. Louis Star (St. Louis, Missouri, USA) of Wednesday 12^th June 1912:

I sat behind Onorato Danesi and Louise last night on the Meramec Highlands car. He certainly was shooting the breeze. “Oh, yes, I’m great on history,” said Onorato, who wore a passionate red necktie. “I am particularly strong on the Revolutionary war stuff. I used to get medals for it at school. There was one great thing about it that I will always remember. [&c.]”

3-: From Military A. & S. C., published in the International Gazette (Buffalo, New York, USA) of Saturday 8^th February 1913:

There are several names for a fellow who lies. He is called a con shooter, bull shooter; they say he spreads the salve, shoots the hot air, he shoots the breeze, etc.

4-: From an advertisement for Arnold & Wetherbee, electrical contractors, published The Daily Oklahoman (Oklahoma City, Oklahoma, USA) of Sunday 24^th May 1914—here, the phrase to shoot the breeze is used literally, perhaps punningly in reference to its figurative meaning:

Our CENTURY FANS Sure Shoot the Breeze

5-: From The Richmond Palladium and Sun-Telegram (Richmond, Indiana, USA) of Saturday 27^th June 1914:

RICHMOND MAN SHOWS UP CHAMP

When G. L. Kinsburg, the Brooklyn checker champ, made the rather large assertion that he would hold his own with a dozen men at one time, “he was not shooting the breeze,” but nevertheless his performance of this stunt was a bit dimmed when one particular G. P. Clawson, a Richmond man, turned the trick on the champ two out of three. Whether Kinsburg was just laying down on his job or not is unknown. Kinsburg claims to be the juvenile checker champ of the world, and is making a tour of the states giving exhibitions of his prowess.

6-: From The Evening Item (Richmond, Indiana, USA) of Wednesday 1^st July 1914:

M’GUIRE MANAGER SAYS NO PROTEST
Conflict Over Pottenger is Heard and To Be Investigated

Once again the sporting writer of another Richmond newspaper was proven to have been “shooting the breeze” when last Monday it was announced that the Dille-McGuire team of the Saturday Afternoon League would protest the game that was lost to the Panhandles at Natco park last Saturday. Manager Winsett in the meeting of the League last night denied that there was any intention of protesting that game.

7-: From the column Sport Salad, by L. C. Davis, published in the St. Louis Post-Dispatch (St. Louis, Missouri, USA) of Tuesday 28^th July 1914:

A Thirteen-Inning Talkfest.

THE shades of night were falling fast.
As o’er Grand avenue there passed
Some fifteen hundred fans or more,
Who looked disgusted, sad and sore.

“Oh, why so sad?” I asked a guy.
He stopped and looked me in the eye
And said: “For dinner I am late,
I’ve been attending a debate.

“At shooting super-heated breeze
Those Senators are all the cheese;
Their play consists of mostly words
And throwing chatter to the birds.

“Those ginks assembled at the park
And talked and talked, till it was dark;
They talked until their tongues were lame.
Then won a thirteen-inning game.”

8-: From the column Sport Salad, by L. C. Davis, published in the St. Louis Post-Dispatch (St. Louis, Missouri, USA) of Thursday 17^th September 1914:

Welcome, Editors.

TODAY, within our midst we find
The molders of the public mind.

The editors from up the State
Have mobilized behind our gate.

We always have a welcome for
Ye gallant country editor.

A fine upstanding bunch of men,
Those wielders of the “facile pen.”

They all observe the Golden Rule
And take their cue from Kelley Pool.

Today our old friend Jimmy Booth
Will stretch a point and tell the truth.

He’ll give an illustrated wheeze
And shoot the expurgated breeze.

We’ll take the boys to see the Browns,
And then, to drive away their frowns,

We’ll take them on a trip to see
Bellefontaine, also Calvary.

9-: From the column Sport Salad, by L. C. Davis, published in the St. Louis Post-Dispatch (St. Louis, Missouri, USA) of Saturday 27^th February 1915:

Legerdemain.

THERE was a man in our town
Who asked us to believe
He had a player of renown
Secreted in his sleeve;
He certainly knew how to shoot
The superheated breeze;
For, when he gave his sleeve a shake,
Out dropped a hunk of cheese.

10-: From the Colorado Springs Gazette (Colorado Springs, Colorado, USA) of Tuesday 29^th June 1915:

Interest in the lawyer-doctor baseball game which will be played Saturday afternoon, July 10, for the benefit of St. Francis hospital, at Washburn field, has reached such a pitch that members of the rival professions have taken to submitting derogatory articles on their opponents to the sport editor of The Gazette. This, for instance, from the medical profession.
“Doc Anderson says if the lawyers bat the ball as hard as they shoot the breeze, the game will be called at the end of the first inning on account of darkness.”

11-: From The San Antonio Light (San Antonio, Texas, USA) of Friday 6^th August 1915:

A Few Minutes With the Sporting Editor

Press agents of pugilists have shown their wares before the peace-loving citizens of the United States these many years but the champion of them all, including Jim Corbett, Jack Curley and lesser lights at shooting the breeze, has been uncorked in Gotham. He is none other than Jimmy Johnston of deah old New Yoik, who now is handling the affairs of Ted Lewis of Lunnon, Hengland.