You can still use a second device travelling through airports. You don't need to carry your daily driver with you, send it to yourself.

It depends on how extreme you want to go and how much data you want to keep in the cloud. Some people operate entirely from the cloud. You can run your own, put Nextcloud on AWS.

About the safest you can do without hardware destruction is to use a rooted phone with unlocked bootloader and run a third party app to erase and over-write partitions of choice. Using TWRP (replacement bootloader) you can make a complete backup of the phone that can be stored remotely and restored with ease. I have done it, it's easy. I kept a backup of my device on a USB drive.

If you have an unlocked bootloader and TWRP there's exploits they can use to access the phone, alas that's no different than if you gave them your password anyway. They will load their own bootloader via USB. It makes it easier for you though. Just be sure to encrypt it, criminals can access TWRP but can't access your files.

I have recovered data from a phone using the same method they use.

I don't know how they would treat the database from a password manager, it's likely they would tell you to unlock that as well whether legal or not, at least that can be stored remotely with ease. You can also put a hardware key in the post to yourself. You can't be forced to unlock it if you can't unlock it. Just know that they can legally hold your device/s.