Why does the paginator go into child sections?

I think what’s confusing is your use of multi-level post type directories. The second level _index.md might be better an index.md. But without a test repo I wouldn’t know. I have quite some paginator use cases, but none where it goes into multilevels with _index.md.

Have a look at this thread here, the docs they talk about might give some hints - I remember though reading it in the final docs already too: