Neo4j Graph Platform | Desktop: System Hardware Requirements

Where can I learn about the minimum system hardware requirements
to use Desktop Browser to visualize graphs with some million of nodes?
In particular, the minimum requirements for the graphics card?

The Desktop browser is not really intended for visualizing millions of nodes. I believe it has an internal cutoff that it won't go above, that is several orders of magnitude lower than this, partially because of the way the browser itself is built. The browser is intended to be an interactive command shell that can help visualize results, but generally it's trying to color code and label things, with limited flexibility there; when you get to millions of nodes you're really needing to look at clusters and hyperclusters of nodes, and you're more interested in the topology of the thing than the individuals themselves; I'd call this a very different use case.

For visualizing large scale graphs, you may want to look at another tool such as Linkurious, Bloom, Gephi, or similar.