Are the supplications mentioned firmly established and sound for bringing sustenance?

If the intent is to establish the first supplication as having been elevated (marfu‘) to the Prophet, peace and blessings be upon him, then no elevated source has been found for it. As for the second supplication, Al-Hakim narrated it in Al-Mustadrak and authenticated it, but verifying scholars such as Al-Hafiz Al-Dhahabi and Ibn Hajar deemed it weak. If the intent is to establish its authenticity from the sayings of scholars or the experience of the righteous, then no such evidence has been found.