Strategy is vision, plan is its implementation.
I think in today's agile world, test plan does not have any relevance as testing is more integrated and dependent with dev activities as done in small sprints.
Although I think test strategy still has relevance as its more about guiding principles(in given context) than actual implementation like test plan.
I agree that test plans typically do not benefit QA Leads, they only serve the customer if the product uses mature tech stacks and processes. That's just not how it works when those things change.
Suppose your test team was testing RESTful APIs using the Postman GUI client on JSON. Then you adopt Kafka with its new data structure (avro) and need an avro ...