Is the waw in "Subhan Allah Al-Adheem wa Bihamdihi" for conjunction, and what is the detailed meaning of this supplication?

The "wa" (and) in "Subhan Allah wa bihamdih" (Glory be to Allah and with His praise) could signify a few things: it could be a "wa" of state (hal), meaning "I glorify Allah while being adorned with His praise"; or a "wa" of conjunction ('atf), meaning "I glorify Allah and I praise Him"; or it could be an extra "wa" (za'idah), meaning "I glorify Allah with a glorification coupled with His praise." The first and second possibilities can be found in the commentaries of Al-Alfiyah, while the third was explicitly stated in Al-Tashil, which mentioned that the abundance of its supporting examples proves its validity.