I did a little more digging and found "What The Left Hand Was Doing" online at Project Gutenberg and user14111's comment has a link to another online copy of the story.
The story seems to be set in about 1984, 35 years after the Communist victory in 1949:
Not even the thirty-five years of Communism, which had transformed agrarian China into an industrial and technological nation that ranked with the best, had destroyed the ancient Chinese respect for age.
And it mentions "the Peiping Explosion":
The Peiping Explosion, back in the sixties, had almost started World War Three. An atomic blast had leveled a hundred square miles of the city and started fires that had taken weeks to extinguish. Soviet Russia had roared in its great bear voice that the Western Powers had attacked, and was apparently on the verge of coming to the defense of its Asian comrade when the Chinese government had said irritatedly that there had been no attack, that traitorous and counterrevolutionary Chinese agents of Formosa had sabotaged an atomic plant, nothing more, and that the honorable comrades of Russia would be wise not to set off anything that would destroy civilization. The Russian Bear grumbled and sheathed its claws.
The vast intelligence system of the United States had reported that (A) the explosion had been caused by carelessness, not sabotage, but the Chinese had had to save face, and (B) the Soviet Union had no intention of actually starting an atomic war at that time. If she had, she would have shot first and made excuses afterwards. But she had hoped to make good propaganda usage of the blast.
The Peiping Explosion had caused widespread death and destruction, yes; but it had also ended up being the fastest slum-clearance project on record. The rebuilding had taken somewhat more time than the clearing had taken, but the results had been a new Peiping—a modern city in every respect. And nowhere else on Earth was there one hundred square miles of completely modern city. Alteration takes longer than starting from scratch if the techniques are available; there isn’t so much dead wood to clear away.
In the middle of the city, the Chinese government had built its equivalent of the Kremlin—nearly a third of a square mile of ultra-modern buildings designed to house every function of the Communist Government of China. It had taken slave labor to do the job, but the job had been done.
A little more than half a mile on a side, the area was surrounded by a wall that had been designed after the Great Wall of China. It stood twenty-five feet high and looked very quaint and picturesque.
And somewhere inside it James Ch’ien, American-born physicist, was being held prisoner. Spencer Candron, alias Mr. Ying Lee, had to get him out.
In real life:
The Forbidden City is a rectangle, measuring 961 m (3,153 ft) from north to south and 753 m (2,470 ft) from east to west.
So the Forbidden City is actually 0.597 miles by 0.467 miles, or 0.279 of a square mile in area, and is not only surrounded by a wall but also by a moat. But the Chinese Communist government was never interested in using it as a seat of government.
And I still don't know how I learned that the story was "What the Left Hand Was Doing" by Randall Garret if I didn't ask the question here before and get an answer.