May I suggest that the reason for all of the confusion regarding bore sizes comes from the fact that although it is true that a .580 sized bore would be marked 24 and a .577 sized bore would be marked 25, those aren't the actual sizes of those gauge numbers.
Here is an edited chart of bore sizes from the Gun Barrel Proof Act of 1855:
The actual sizes are 24 =.579 and 25 = .571.
I assume that any contracts issued by either US or CSA would have specified the rifled caliber rather than the markings, while the bore size markings were from actual measurements and were applied to satisfy the British commercial proofing laws and relied upon standard gauges of the sizes indicated in the chart.
The Proof Act specifies that a "Set of Standard Plugs" would be used to measure barrel sizes. Working from the numbers specified in the chart; a 24 gauge plug measurement would correspond to a bore from .579 - .586 and a 25 gauge plug measurement would correspond to a bore from .571 - .578.
Just because the British proof act specified gauges of 24 or 25, it doesn't necessarily follow that US or CSA contracts had any relationship to those numbers. I think that the idea that 24 = .58 and 25 = .577 is a modern construct that wouldn't have been recognized at the time. 24 and 25 meant the numbers in the British proof act, .579 - .586 and .571- .578 respectively. .58 falls at the very low end of the 24 range, and .577 falls at the very high end of the 25 range. Consequently, overlap of the two calibers in practice, when measured by the British gauges, seems obvious to me.
Thus, a slightly undersize .58 bore or slightly oversize .577 could have either 24 or 25 marking and probably still fall within the specifications of the contract. I have no idea how strict those contracts were, but considering what we know of the general scramble for arms it is hard to imagine that they were being very picky about it.
I have never seen a Civil War era drawing or document that specified what kind of tolerances were acceptable back then, if anybody has something like that I would love to see it. I presume they didn't actually specify them on drawings the way we do now, but clearly they were using gauges so there was some sort of system of determining what was acceptable.
I used to be a mechanical engineer working for the US Navy. We typically considered +/-.010 to be a "loose" tolerance, and +/-.005 to be "tight." Obviously, we could go tighter if the application demanded it, but we tried to avoid it. I say this just to put in context that the difference between .577 and .58 is only .003, less than what we considered a tight manufacturing tolerance over 100 years later. I'm sure they wanted bores to be rifled as perfectly as possible, but there had to be some sort of tolerance allowed, which presumably would have included some degree of overlap between .577 and .580 bores.
Let me give an example. I have no idea what tolerances they actually allowed, but suppose it was -.002/+.005, which I think is a very reasonable guess. It also provides a tolerance range from low to high of .007, identical to the tolerance range indicated in the British gauges. That would translate to an acceptable .577 bore being from a low of .575 to a high of .582, and a .580 bore would be from a low of .578 to a high of .585. Thus, there would be a range of overlap between the two calibers from .578 to .582. What's more, that would also include a range of overlap with both 24 and 25 bore sizes in the British Proof Act, with .579 and up being 24, below that being 25. In other words, my hypothetical example would include potential markings of 24 and 25 on acceptable examples of both .577 and .580 barrels.
The full proof act can be found at:
https://www.legislation.gov.uk/ukla/Vict/18-19/148/enacted