A private-window sign-in is not the same as testing account recovery, and I would not make major security changes the night before leaving. Some services place delays on newly added phone numbers, recovery contacts, passkeys, or security keys. Others treat a new country, unfamiliar browser, and recent settings changes as suspicious. A backup method that appears in your settings may not be usable immediately.
The safer approach is to set everything up well before the trip, then verify it without dismantling the working setup. Check that you can open your recovery email from another device, confirm that printed backup codes are still current, and make sure a second security key actually appears on the account. If you regenerate backup codes, remember that the old set usually stops working. Label the new set with the account name and generation date so you do not end up carrying an obsolete page.
Synced passkeys and backed-up authenticator data can make replacement much easier, but they create another dependency. If the credentials sync through your Apple, Google, or password-manager account, you still need a way into that account without the lost phone. Being signed in on a tablet is useful. Knowing only that “it should sync” is not a recovery plan.
I agree with the general advice to preserve a usable session, but do not assume support will quickly override two-step verification if every backup fails. Recovery can involve waiting periods, old billing information, identity checks, or a flat refusal when the service cannot verify ownership. For smaller accounts, there may be no human recovery route at all. Save basic account details outside the phone, including usernames, recovery addresses, customer numbers, and which method protects each account. Do not include passwords on an unencrypted sheet.
If the phone disappears, your accounts normally remain intact. The practical question is whether the phone was merely lost or may be accessible to someone else. With a locked device, you may have time to use another session and enroll the replacement. With an unlocked or compromised device, protecting email, the password manager, and the mobile number takes priority over keeping convenient sessions alive.
The best setup is boring: two independent ways back into the few accounts that control everything else, arranged early enough that any security delay has already passed before you travel.