The "Build Balances Zones" was introduced in ArcGIS Pro 2.4 and allows a kind of spatial clustering with the help of genetic growth algorithm:
The Build Balanced Zones tool uses a genetic algorithm to create spatially contiguous zones in your study area based on criteria that you specify. You can create zones that contain an equal number of features, zones that are similar based on a set of attribute values, or both. There are also options to select zones with approximately equal areas, that are as compact as possible, and that maintain consistent summary statistics (such as averages and proportions) of other variables.
Is there an equivalent to this in QGIS? I tried "Attribute Based Clustering", but this gives quite different results. Apart from that I did not find any similar tools.
I would like to use it on a population map, creating zones with 1 Million people in each zone. Similar to a census map, but worldwide.
Cluster Analysis
(in the Processing Toolbox). It sounds like it might do what you want, but then again so did the plugin you already tried, so who knows. If the SAGA tool doesn't work for you, maybe you could elaborate on what was different/wrong with the results of this and the plugin compared to the ArcGIS tool.