This flag was proposed by some members of Russian opposition after the conflict war in Ukraine started. By taking the red (bloody, communist, hostile) colour out of the flag and by replacing the blue with the lighter azure colour, they want to promote the idea of the new Russia as a modern democratic republic.
There were a lot of talks that this flag is based on the flag of the Novgorod republic, which is considered to be the first Russian republic in history. I have not been able to confirm this until now (2022-08-22).