First things first: I know I could use CHKDSK or any other third-party tool to detect bad sectors but this question is especially dedicated to whether a "Full Format" on modern Windows systems checks for bad sectors.
I've found this answer which says:
When you choose to run a regular format on a volume, files are removed from the volume that you are formatting and the hard disk is scanned for bad sectors. The scan for bad sectors is responsible for the majority of the time that it takes to format a volume. source
In Vista and later, this is accomplished by writing zeros to the entire partition.
The link for the first quote to the Microsoft pages is dead, the link for the second is alive but only says this (emphasize mine):
"The behavior of the format command changed in Windows Vista and later Windows versions. By default in Windows Vista and later versions, the format command writes zeros to the whole disk when a full format is performed. In Windows XP and earlier versions of Windows, the format command doesn't write zeros to the whole disk when a full format is performed."
Microsoft only speaks about that in any modern Windows version beginning at Vista doing a "Full Format" would perform a complete zero-write to the hard disk, but they do not say that the zero-writing process would be connected to a check for bad sectors.
What I am basically looking for is an alive link to the first or any similar quote from Microsoft itself, confirming a "Full Format" on any modern Windows (7, 8 and/or 10) system would perform a bad sector check by writing the zeroes OR any proof that it does that (maybe by personal experience).
Thank you for your time. Any help appreciated.