Assuming there are no other numbers in the directory path, you could use
exiftool "-AllDates<$Directory 00:00:00" /path/to/files

That would set the EXIF timestamps to midnight on the date in the filepath.

If there are other numbers in the directory path, then a complex command would have to be used. Assuming the date is exactly as you posted
exiftool "-AllDates<${Directory;m/(\d{4}-\d\d-\d\d)/;$_=$1} 00:00:00" /path/to/files

These commands cannot be run from that directory, i.e. using a dot to indicate the directory. They must be run from above that directory using the -r (-recurse) option or must include the date as part of the indicated path, e.g. /path/to/2003-01-22/.

This command also does not affect the file system time stamps. To set those as well, duplicate the center part but replace AllDates with FileModifyDate or FileCreateDate.

This command will overwrite any existing timestamps, so make sure you're processing the correct files (see the -wm (-writemode) option for ways to alter this). This command creates backup files. Add -overwrite_original to suppress the creation of backup files. If this command is run under Unix/Mac, reverse any double/single quotes to avoid bash interpretation.