From a time-series point of view, an anomaly could be defined a value that doesn't fit most known patterns.
Now, we should define the time range and the method to detect the anomalies, and it depends on the data you are using.
For instance, if you have a very simple business case to detect abnormal peaks in a short time range, you could merely set the average value from the 10 last minutes and set a threshold (ex: +50% of the average value) that would detect an anomaly.
For simple shapes' detection in short-term time series, you could apply first (and potentially second-order) derivates to detect simple variations and also apply a threshold.
But if you want to detect complex shapes in longer time ranges, you can apply unsupervised time-series clustering but it is only applicable if your date has some cyclic behavior (otherwise you couldn't detect the start and the end of each time frame).
Some non-linear algorithms like PacMAP or UMAP could generate very clear clusters and detect outliers easily.