Well, I have the feeling that the view about which role the military plays in the context of climate crisis has changed a lot within the last years. A lot of climate and security organizations have been founded, many of them run bei retired militaries. I'd say that they are aware that the military can't be the "solution", but they have realized that their work will be highly affected by the consequences of climate change. We might need them for more disaster relief operations or when tensions and conflicts are increasing. Speaking of that, some think that militaries are a good "alarm bell" to warn about climate crisis, making those listen that actually wouldn't get interested in climate change. Others think that it's getting dangerous when the impression is created that we can solve problems just by raising our defence budgets...
This leads to your second question: As the military can't be the solution, we need any other part of society to fight for stopping our emissions. All the organizations that you're mentioning - political actors, activists, economists, teachers, young and old people, etc. etc. can and will play an important role if we want to stop our planet from heating up.

Regarding your own engagement: There's no right or wrong way of course, but it should be all about reducing emissions. Not just on an individual level, but - much more important - on a big scale. I think it's always helpful to ask yourself in which area you could generate the biggest impact and put pressure on climate action: Your school, university, workplace or local politics could be good places to start. It might feel like it's not enough, but just imagine each company, school, organization and town would have someone taking care for them becoming climate neutral...