I second the answer by @StephanKolassa. Also note that none of the tests and methods cited by you takes the time series structure of your data into account, which should be done if (a) you want to detect full time series that are outlying w.r.t. the overall set of series or (b) you want to detect an outlier in a single time series w.r.t. the other values in the same series, independently of other series. IQR and the tests above only make sense if the task is to detect an outlier at a given fixed time point where one series may be outlying w.r.t. the values of the others.
That said, you are right to question the use of the formal tests vs. IQR in practice, where these tests are not that often used. Note in particular that the tests start from the assumption that the non-outliers are normally distributed. Note that this should not be tested in advance using QQ-plots or normality tests like Shapiro-Wilk (as somewhat misleadingly recommended in the cited document), because it does not mean that the data overall are normally distributed (at least not if they have outliers). What it means is that the normal distribution is used as a "reference distribution", i.e., it relies on the decision of the user to brand observations outliers that deviate from normality in the "outer regions". The normal distribution is some kind of standard choice as "non-outlier reference" (the justification of which is a rather complicated and controversial issue), because it has most observations in the middle and observations far away form the mean (in terms of standard deviations) are very unlikely, but it may be inappropriate for example in case of essentially skewly distributed data. The choice of reference distribution should be made based on knowledge what kind of data behaviour is "standard" and how relevant "outlyingness" plays out in the given specific situation. Many choose the normal distribution without thinking much about this, which may or may not be appropriate. For the problem of detecting an outlier in a time series, the reference should probably be a time series model or something that takes the time series character into account.
Based on the normal distribution assumption, the tests will check whether the most extreme observation(s) are in line with what is expected in the extremes of the normal distribution. Under this assumption the tests can guarantee the chosen significance level as type I error rate, and via a p-value they can formalise how sure we can be that certain extreme observations deviate from normality. This is useful information in some applications and is not given by the boxplot rule, but note that just the fact that an observation deviates from what would be expected under normality doesn't necessarily make this point "problematic" or "special". Particularly with big data sets it doesn't even need to be particularly far away from the rest to be branded "outlier"; it is enough if the standard data generating process deviates somewhat from normality, which very often happens in practice. (Note that outlier identification also needs to depend on what the consequences are, i.e., do you want to remove all observations identified as outliers - often a bad idea -; would you do some steps to check how they came about to see whether they are OK - often a better idea?)
The boxplot rule is a quick exploratory tool, which can also be interpreted based on normality. For large numbers of observations from a normal distribution, it will identify somewhat less than 1% of the data as outlier. It is constructed to not rely that strongly on normality, but still has some "similar-to-normal" characteristics (basically there should still be more concentration in the middle, i.e., between first and third quartile, with density going down toward the outer regions, and the principle to identify outliers is symmetric; see Stephan Kolassa's answer for an example where this goes wrong). It is nice in many situations as a first orientation, but there is no guarantee that boxplot-outliers are "bad" or should be deleted. Still for first exploratory analysis its information is usually practically more useful (if not overinterpreted) than what you get from the formal tests.
