Does the Friday supplication circulating in technology, which begins with "O Allah, Owner of all sovereignty, and Giver of immense bounties...", have any basis in Islamic law?

This supplication has no basis in the books of Sunnah or from the early Muslims (Salaf). It appears to be from the كلام (sayings/writings) of contemporary people. It is a good supplication that does not contain any violations, so there is no harm in supplicating with it, provided one believes that it is not authentically transmitted and does not attribute to it any specific virtue or commit to it at a specific time, in order to avoid falling into an additive innovation (Bid'ah Idāfiyyah).