How long does it take to open a company bank account in Uzbekistan?

Which clock applies turns on residency, not on who owns the company. A company incorporated in Uzbekistan is a resident legal entity however foreign its shareholders are, so the next-working-day duty is the one that reads on it. The fifteen-day clock is for the non-resident clients the instruction lists separately — representative offices, permanent establishments, exchange participants and the like. (Bank Accounts Instruction, Paras. 6, 16 — lex.uz ↗)

That is the deadline the act imposes on the bank once the documents are in. It is not a promise about how long the whole exercise takes: the compliance questions come before the documents are accepted, not after, and that is the part with no deadline attached to it.