Quoting this article https://docs.microsoft.com/en-us/windows/desktop/FileIO/naming-a-file#maximum-path-length-limitation
Maximum Path Length Limitation
In the Windows API (with some exceptions discussed in the following paragraphs), the maximum length for a path is MAX_PATH, which is defined as 260 characters. A local path is structured in the following order: drive letter, colon, backslash, name components separated by backslashes, and a terminating null character. For example, the maximum path on drive D is “D:\some 256-character path string<NUL>” where “<NUL>” represents the invisible terminating null character for the current system codepage. (The characters < > are used here for visual clarity and cannot be part of a valid path string.)
Now we see that it is 1+2+256+1 or [drive][:\][path][null] = 260. One could assume that 256 is a reasonable fixed string length from the DOS days. And going back to the DOS APIs we realize that the system tracked the current path per drive, and we have 26 (32 with symbols) maximum drives (and current directories).
The INT 0x21 AH=0x47 says “This function returns the path description without the drive letter and the initial backslash.” So we see that the system stores the CWD as a pair (drive, path) and you ask for the path by specifying the drive (1=A, 2=B, …), if you specify a 0 then it assumes the path for the drive returned by INT 0x21 AH=0x15 AL=0x19. So now we know why it is 260 and not 256, because those 4 bytes are not stored in the path string.
Why a 256 byte path string, because 640K is enough RAM.