Fix the inclusive day count for billing

A legacy billing helper subtracted two timestamps and divided by a day's milliseconds. An AI described it as an inclusive day count, but it returned 2 for January 1 to January 3, and daylight saving days broke it further. The replacement works on calendar dates only and counts both endpoints.

An assistant wrote inclusive_billing_days(start_date, end_date). It is in the editor. It has a bug. Find it and fix it.

Input and output:

• start_date, end_date: dates as "YYYY-MM-DD" strings.
• Return the number of billed days, counting both endpoints.

Rules the tests check:

• Each date must be exactly 10 characters: 4 digits, -, 2 digits, -, 2 digits. Otherwise return 0.
• Each year must be 1 or more, each month 1 to 12 and each day 1 to 31. Otherwise return 0.
• A day past the end of its month counts on into the next month, so 2026-04-31 is the same day as 2026-05-01.
• Use the Gregorian calendar. A leap year is divisible by 4, except a year divisible by 100 is not a leap year unless it is also divisible by 400. So 2000 is a leap year, and 1900 and 2100 are not.
• If the end date is before the start date, return 0. Otherwise return the number of days from start to end, plus 1.