Again on "Either"... does it mean "both"? [duplicate]

Either does not mean both when it expresses an alternative. The required conjunction is or, never and.

Thus you need to provide one or the other; this is confirmed by the context, which is the requirement to show a QR code. Each form of the document has that, and you only need one form of the document to satisfy the requirement. The government's web page would certainly be improved by adding an or to the first alternative. However, to put and there would not make sense at all.

Either in "It could be on either side of the street" does express an alternative: it's assumed that of two possibilities, only one will apply. That doesn't mean "It could be on each side of the street," it means "It could on either this side of the street or that side." You can't say "It could be on this side and that side" when only one is possible.

Either in "There are shops down either side of the street" does not express an alternative: it actually has the same meaning as each side and does indicate that both sides of the sides of the street have shops. But that meaning is only possible because there is no either/or alternative.