Yes, the T2 always "remembers" its unique ID (ECID) even if you turn Full Security off and on again. It is never discarded.
However, this is really not the question you would like to be asking:
The ECID is burned into the T2 chip and cannot change. The actual signature file created when the operating system is installed is stored on your disk drive as an ...
No, the T2 cannot in any way be used as a TPM for BitLocker. TPM for BitLocker is not a generic term for any type of trusted platform module, but rather it needs to be specifically the Intel TPM specification (latest version is 2.0). The T2 chip does not work in a way compatible with the TPM specification.
I’ve had issues with my touch bar too. (See Touch Bar not turning on after waking computer from sleep.)
Here are some things that didn’t work for me, but they might work for you:
Open Activity Monitor, find and select TouchBarServer, then press the Stop button. Then select Force Quit. It should restart automatically and your touch bar should be back to ...
Use “Migration Assistant” instead of attempting a direct restore. This mitigates hardware change issues, T2 issues, minor OS difference issues, some software licensing issues, and a few other potential issues.