Is there a limit to the number of clusters (providers) that can be connected and managed by a Enterprise Team Center? I'm not asking for sizing, just if there's a limit to the number of providers (similar to the 10 collector limit for a MOM)
There is no limit. The limit/speed is mostly defined by connection speed to providers, size of data in providers and speed of database in ETC. Best guess is to sum up vertices of providers before join. These should be under 50k.
Note: If you go beyond the four providers, the performance of ETC might/will be severely impacted.
All the vertices, edges, attributes and ATC events/status are kept in the APM DB of the ETC. Follow recommendations in the documentation and keep an eye on the database query times and vertex, edge counts and history size! Use Solid-state drives (SSDs) for APM DB!