Was expecting the article to go more in-depth.

Say, what happens when chain of summaries grows so long, that it still overflows context window. Is summarization runned over the summaries in the context window?

What more depth is there to go to? Compaction is a single LLM call (practically) which can have some deterministic diffing/extraction baked in, or multiple LLM calls (generally wasteful). There's only 1 summary in the context window at one time. Every prompt goes [CONVERSATION_HISTORY] + input -> model turn. As soon as total context exceeds that it compacts, so there's no summarisation overflow (you can enable an agent to access past summarisations from past compactions, but the snake starts to eat it's own tail).

There is no chain, just a lossy summary that includes a summary of any previous summary along with the fresh messages.