So there’s the zscore formula with only sigma as denominator, and there is one with standard error as denominator

I know you use the standard error one for hypothesis testing, but what about the former? maybe for questions where sample size is not mentioned at all?

You use σ in the denominator when creating confidence intervals or testing hypotheses about a random element in a population (e.g., next month’s bond return); you use standard error (= σ / √_n_) in the denominator when creating confidence intervals or testing hypotheses about the mean of the population.

The standard error can be viewed as the “standard deviation of the SAMPLE mean”. It’s used when you are conducting hpotheses tests using the mean of a SUBSAMPLE of the population.