The meaning of the word "stretched" in the sentences in bold is ambiguous to me

Question

They had come to fire the house, their visit expected because they had been before. On that occasion they had come later, in the early morning, just after one. The sheepdogs had seen them off, but within a week the dogs lay poisoned in the yard and Captain Gault knew that the intruders would be back. ‘We’re stretched at the barracks, sir,’ Sergeant Talty had said when he came out from Enniseala. ‘Oh, stretched shocking, Captain.’ Lahardane wasn’t the only house under threat; every week somewhere went up, no matter how the constabulary were spread. ‘Please God, there'll be an end to it,’ Sergeant Talty said, and went away. Martial law prevailed, since the country was in a state of unrest, one that amounted to war. No action was taken about the poisoning of the dogs.

Does the first sentence in bold mean: we have lack of soldiers? or We are so busy at barracks?

and so "stretched shocking" mean: being busy is really shocking? or lack of soldiers is really shocking?

Source: The Story Of Lucy Gualt by William Trevor.

Answer 1

You are creating a false dichotomy. If the number of soldiers was 1 and that one had nothing to do all day, they would not be “stretched.” If the number of soldiers were 100,000, and each was already on active duty 21 hours a day, they would be “stretched.” The idiom does not relate to the number of people, nor does it relate to the required hours of activity. It indicates that the number of people available is scanty relative to the number required.

In context, it very much looks as though “shocking” is intended ironically. The speaker recognizes that the soldiers are fully occupied and may be disapponted but not surprised by the lack of support.

Answer 2

It could mean either or both.

You would need to interrogate the speaker to be sure what they mean.

Answer 3

Yes, lack of soldiers. Adding "shocking" emphases the lack, thus meaning many more soldiers are needed. You might substitute the phrases "we are understaffed at the barracks" and "oh badly understaffed" (in the UK the phrase "sorely understaffed" might be used).