Sounds like you've done an excellent job
Yes, if the airbag wasn't wired up properly or it was replaced with the battery connected, then you would have the airbag warning light on.
and if, like me, the steering angle sensor (G85) wasn't properly lined up, the ABS and ESP lights would be on
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Present: S4 B8 avant, fully loaded, MRC Stage2, Milltek non-res, KW springs
Past: S8 D2 FL, S2 ABY coupe, RS6 C5 saloon, RS4 B7 saloon, S4 B5 saloon, S4 B6 avant, all gone but not forgotten