These are standard changes. "Backdoor ii V" or "backdoor cadence" is a term for a ii V that would resolve to the bIII but resolves to the I...you could write it as iv7 bVII7. It's very common, as is the temporarily modulation to bIII in the fifth bar, as is the minor ii V (iim7b5 V7b9) that resolves to a major seventh in bars six and seven.
In this specific case it's a mix of key centers - G and Bb, G minor being the relative minor of Bb major.
It's hard to answer the question of how I'd approach these changes, as they are so typical. It depends on the melody, the style of the tune, who I'm playing with, what the tempo is, etc.
People are probably going to say "G major | C dorian, F mixolydian " etc or maybe "G major | Bb major " etc, and that's apt too, but if we're talking about jazz as I understand the term, it's sensible to have ii V I vocabulary and know how to use it, or at least see the guide tones in this progression.
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