In general, if I imagine ‘longtermism’ taking off as a term, I imagine it getting a lot of support if it designates the first concept, and a lot of pushback if it designates the second concept. It’s also more in line with moral ideas and social philosophies that have been successful in the past: environmentalism claims that protecting the environment is important, not that protecting the environment is (always) the most important thing; feminism claims that upholding women’s rights is important, not that doing so is (always) the most important thing. I struggle to think of examples where the philosophy makes claims about something being the most important thing, and insofar as I do (totalitarian marxism and fascism are examples that leap to mind), they aren’t the sort of philosophies I want to emulate.
Maybe this is the wrong reference class, but I can think of several others: utilitarianism, Christianity, consequentialism, where the “strong” definition is the most natural that comes to mind.
Ie, a naive interpretation of Christian philosophy is that following the word of God is the most important thing (not just one important thing among many). Similarly, utilitarians would usually consider maximizing utility to be the most important thing, consequentialists would probably consider consequences to be more important than other moral duties, etc.