How do you motivate teams on death march projects?

+1 to this question.

What should you do when leadership says “this is wartime”?

That's a tricky situation. I guess you certainly tried to push back the timeline and the leadership didn't care. I'd focus on what you can do within your team.

1. More team building events like offsite, go karting, coffee chat hours, etc...
2. Try some pep talk in your one on one with your teammates.
3. Maybe just some small talks before standup to help people feel connected
4. More praise in PR review and more kudos to anything.

I know my suggestions are cheesy and clearly avoid the crux of the problem (tight deadline), but here's my mental model. Suppose your team's satisfaction level is 30%±20%. The 30% is anchored by your leadership and organization. The ±20% is under your control. As a team lead, if you can achieve the upper range of the spread, I'd say you've done a good job in terms of manager satisfaction.

Leadership wanted this project done in 3 months, but it ultimately took 6 months.

Good thing is they probably know 3 months is not a realistic timeline, so don't burn yourself out. Also for my curiosity, what was the planning process for that project? Did you first present a 6-month plan and then leadership asked to cut scope to find a 3-month launch plan and then by the time it hits 3 month, the project is delayed month by month until it hits the 6-month mark?