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Let's suppose I have done the most I can to secure my phone on a software level (e.g. encrypted storage, restricted app permissions ... whatever you consider "maximally secure"). Is physical access still game over?

It is very trendy to say "everything can be hacked", but in your case the game is not over. Mobile OS enables much more security hardenings than PC:

1. Secure OS (see ARM TrustZone).
2. Specialized security chips (see Secure Enclave).
3. SELinux.
4. No root.
5. Containerization.
6. Disk encryption.
7. ASLR, KASLR.
8. and much more...

And this is a baseline for iOS and Android in 2020.

Let's consider the basic way how data is protected in a modern mobile OS:

1. You set a password
2. Password -> symmetric key
3. Key -> encrypted storage

Considering you have done the most you can to secure your phone, there are 2 options to access your phone:

1. brute-force your password (a guessed password means an access to your data)
2. do a factory reset (you loose data, but data remains confidential)

Offline attack

Let's say, if operating system doesn't save your password on disk as a plain text, and your mobile device has been rebooted (so keys don't stay in memory): your data is safe. It means that offline attack is almost impossible. (I said "almost" but it also means the game is not over yet).

Therefore to be sure about data confidentiality, be sure you do your best:

1. Choose a difficult password/PIN
2. Don't forget to lock your device with any kind of credentials

Real world example

There are "magic tools" like dr.fone which claims to unlock any phone without a data loss. Now take a look at their guide with an iPhone 7 case:

Please note this unlocking process will also wipe the data on your iPhone/iPad. Honestly there is no solution to bypass iPhone/iPad lock screen without data loss for the moment in the market.

Another case is that Android cannot decrypt files before you unlock it after reboot, because Android doesn't have a key physically: https://source.android.com/security/encryption#full-disk

Runtime attack with physical access

Here adversary have some options to win the game.

1. If you forgot to lock you phone, having a short physical access adversary can jailbreak (root) your phone, install a back door, and later get everything he needs remotely.
2. If operating system didn't shut down yet, then having theoretically unlimited resources, attacker can try to find encryption keys in memory, and it would be OS vulnerability. A chain of vulnerabilities is needed depending on OS version and a state of security hardening.

To be sure you did everything to mitigate such types of attacks:

1. Lock your phone.
2. Update your OS (particularly do security updates).

And yes, theoretically there is no absolute security: OS may just not encrypt files, or it may leak encryption keys, even cryptography is based on a relative difficulty to solve a particular mathematical problem, or on difficulty to attack a particular cipher... But the game is not over.

SPECIAL UPDATE for people saying "zero days, FBI, dark market, everything can be hacked" and for people who upvotes them.

You cannot just throw these words here and there. It means nothing out of concrete attack chain. TLS 1.3 is not easy to "hack" (that's why you use https), it's not easy to find a collision for SHA-256, it's not easy to exploit the collision, and "not easy" means an enormous time, from a several years to infinity, where CSI will "hack" you physically rather than hacking your phone.

Questioner made a precondition: a concrete case, hardened mobile phone, where he did everything he was able to do. Having this particular precondition I would propose to try to discuss very specific cases. But "it depends on" would be a pretty comfortable and universal answer for sure.