I uploaded the file to ida pro. If I find the immobilizer data, will the cross-references lead me to the immobilizer function? Or maybe you can tell me what else might lead me to the immobilizer?
I've definitely seen at least one s4b5 with a 6hp19a where the immobilizer was disabled in the TCU.

doesn't it have code compression enabled in some code sections? does IDA deal with it or you're decompressing yourself?

I unpacked it manually. It looks like the immobilizer data is in an accessible format, and there are two conditional jumps. At first, I thought that by replacing one of them with an unconditional jump, I could bypass the immobilizer, but it's not that simple. Unfortunately, I have limited knowledge, and I don't have the A2L for this TCU to load the file correctly in IDA Pro. However, I have high hopes that something will work out.

It does look like it's compressed (has several BOSCH AE/EWG TC19.11 MPC562 CC_ON BS1002041270H00138 BDM_RBWERKBSBB1002) (meaning that the code is stored in the compressed form inside the TCU and then decompressed online as it gets executed). In your screenshots, you have some string bytes disassembled as code, I don't know if that's something you wanted to do intentionally or IDA did it on its own.
Maybe you're right about immo routines, and they might be in the section with no compression near BSBB1002BOSCH TC19.11 MPC562 CC_OFF BB1002041270H00157BDM_RBWERKDEVELOPSERIES_BDM_RBWERKCHANGED_FROM_DEVELOP_TO_SERIES, but they're probably called from somewhere in the compressed section(s)