[POBEP]

There were 2 generation of TPMS sensors (not to be confused with FTM) for E9X. Both are 433Mhz. These sensors are NOT interchangeable.

My 2009 E91 LCI uses older version, 2011 E90 LCI & 2013 E70 - newer.
The split date varies by E9X model. For E91 it was mid 2009

I tried to swap E91 / E90 wheels and it did not work (for me)

My E70 has 2 set of wheels summer and winter.
I swap between them with a simple TPMS iDrive reset without an issue.

OE & HUF sensors are known to be auto-magically learned by car computer.
Other brands may need additional effort to be registered

The realoem P/N references are very confusing.

Hence, relevant HUF P/N instead
RDE048V21 - "older" <- these should work for 2007 MY
RDE012V21 - "newer"

as already noted above, your options are
- decent scanner that will help diagnose root cause.
- move original sensors to new wheels.
- buy new set of TPMS sensors
- code car to use FTM
- ignore the issue

I could not "afford" OE and do not want to mess with cheap ones.
Hence, I use HUF as less expensive OE alternative