The Qualcomm chip used in the FP4 lists several relevant hardware-based security features:
On-Device: Qualcomm® Mobile Security, Key Provisioning Security, Qualcomm® Processor Security, Qualcomm® Content Protection, Qualcomm® Trusted Execution Environment, Camera Security Secure Camera, Crypto Engine, Malware Protection, Secure Boot, Secure Token
So yes, basically any modern phone has some kind of TPM that is specifically designed to be able to perform cryptographic operations in a secure manner without ever leaking the key. So assuming the Software uses it properly and there are no design flaws in the hardware, it won’t be able to retrieve the encryption key with everyday methods.
A different tool won’t help you if you aren’t able to access the key used to encrypt your device. Let’s just assume you did a bit-by-bit backup of all the data. Now at some point along the way you decide to do a factory reset, which also regenerates and overwrites the encryption key. Once this happens the stuff you backed up is just some garbled, encrypted mess. Even if you write it back bit- by bit the device won’t be able to make use of it, since the encryption key no longer exists.
Just stick to doing backups the ‘regular’ way and resetting the system using a factory reset (of a full flash using a factory image if necessary). You’d need to compromise your own devices security significantly and in ways that are not permitted by Google’s current security policies to make your backup strategy work as far as I can tell.
(Btw, if you encrypt your linux-laptop using a secure TPM you’d have the same problem if the TPM were to be reset somehow.)
Well, if your partitions are damaged or you f’ed up some deep system sh’t (while experimenting with rooted custom ROMs for example), you may need to perform a full flash using a factory image. But that’s usually not necessary. If a backup as described above were to work, it’d come closer to that than a factory reset I guess. Also you would be able to skip some basic setup steps using the backup-method I guess.
Edit: I just noticed you are talking about the FP5, but the argument should still stand.