Generally, opening a local bank account tracks your residency status, not your nationality. Tourists on short visits usually can't open standard accounts in most countries, since banks want proof you actually live there: a residence permit or long-term visa, a local address, and often a tax identification number. Expats with work visas, student visas, or residence permits can nearly always open accounts, and in fact usually need to for salary payments.
There are exceptions in both directions. A few countries allow non-resident accounts, sometimes with higher minimum balances or limited features, and some banks in expat-heavy cities have dedicated newcomer programs that accept a passport plus employment contract before the residence card arrives. Conversely, some places are strict enough that even residents wait weeks for compliance checks, especially with certain nationalities affected by international reporting rules.
If you're in the gap between arriving and getting residency, multi-currency fintech accounts can bridge it for receiving and spending money.