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. to 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 starts 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-Wilks (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.

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 Kolassas 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.

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.

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.