Continuity mistake: The sketch that Brainy shows to Winn is meant to be his original sketch that he drew in the previous episode, hence why Winn is so shocked he's somehow got it. But it's slightly different from what we actually saw him draw at the time.
Answer: For one, it's usually cheaper to film in Vancouver because of the tax breaks. But all the CW Arrowverse shows (with the exception of "Black Lighting") are/were filmed in Vancouver. So it makes it easier and cheaper for sharing set designs, crossovers, etc ("Black Lightning" filmed in Vancouver during its crossover). Originally "Supergirl" wasn't part of the Arrowverse when it was on CBS, but it was too expensive to produce and wasn't reaching the wider audience the CW shows had. So CBS moved it to its sister company, The CW.
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