Tried the 2FA app instead of texts and got locked out of my own bank

I finally switched my bank login to an authenticator app about 3 months ago, figuring codes by text were too easy to grab. Everything was smooth for a bit, then my phone went for a swim in a puddle on a rainy Tuesday in Cleveland and the backup codes? Still sitting in a drawer at my place, useless to me at the branch counter. Took 40 minutes on hold with support and a trip to the actual branch to get back in. What I learned is that the app is probably safer, but a printed copy of the backup codes in my wallet would have saved me a whole afternoon of hassle. Now I'm wondering if hardware keys are less of a headache for the next step. Does anyone actually carry the backup codes around or do you just trust the app?