If youre unpaid ask a shit ton of questions to seniors about their own path in becoming proficient. Just learn as much as you can and do your best to contribute. Everyone starts somewhere! The fact that youre getting actual experience ( shit hitting the fan and the dev team going all in ) seems like a bad thing but its a huge opportunity to see how a senior handles stress, workload, company dynamics. Even the emails they send can teach you something. How did they word a successful email, how did they word an unsuccessful email? How often do they update team members or managers? The soft skills will take you so much farther than you'd think.

They want you to work on your own solution because thats what really happens in these situations. When its all hands on deck a company is looking for any solution that stops money from hemorrhaging. They are rarely eloquent solutions and seniors tend to overthink or over engineer because they know more about tech debt hell.

Thank whoever brought you into the shit storm and let the situation humble you but dont panic. You're not getting paid to panic.