I don’t have an RS6, but instead have a 2001 Audi A6 2.7T 6-speed, but I wanted to mention that you may have a few options:

You might install ‘EGT Deletes’ which are modules plugged into the EGT connectors on top of the engine for the EGT that is not working correctly, and it will then send a safe temp reading to the ECU, but you lose the safety that the EGT gives if the temp is actually too high. The install is easy, and I’ve installed a few of these on 2.7T’s, and they used to cost say $50-60 for a pair using the forums (QuattroWorld or Audizine) or E-bay. Some of the past sales and discussion for the 2.7T EGT deletes was at https://forums.quattroworld.com/clas...gs/28193.phtml, but I’m not sure if the RS6 could use the exact same EGT delete or if it would be different. On E-bay, nothing appears if I search for ‘EGT delete’, but searching for ‘EGT limp mode’ shows one listing for around $110, but it is for a 2.7T instead of the RS6 engine.

You might choose to open the EGT connector case under the hood, and resolder the board(s) like https://www.rs6.com/showthread.php/3...ir-with-photos or https://www.rs6.com/showthread.php/3...fix-(old-news) or https://www.rs6.com/showthread.php/31959-EGT-Sensor or maybe replace the old boards with new boards like https://www.audiworld.com/forums/2-7...r-good-2850845. I’ve never bought EGT boards from SID Motorsport in Poland, but I took a look, and he does list some for the C5 RS6 at
https://sidmotorsport.pl/index.php?i...roller=product

Note – when I was just looking at the SID Motorsport website, I clicked on a button so the info is shown in English, but when choosing the auto type, the last range (Zakres) info was still in Polish, so I translated the choices, and they are:

CHLODZENIE - Cooling
DOLOT - Intake
HAMULCE - Brakes
INNE - Other
NADWOZIE - Body
NAPED - Drive
PAOLIWO - Fuel
SILNIK - Engine
WYDECH - Exhaust
ZAWIESZENIE - Suspension

You might be able to splice the wiring so the EGT that is working OK will send its info for both banks like is mentioned at https://www.audizine.com/forum/showt...ir-EGT-sensors, but again you lose the safety net if one bank is actually too hot.

If you decide to install a new EGT, then I’m not sure how many places you could get it from, but it looks like it may be available at https://www.the-tuner.com/en/product...tursensor-agt/ which mentions that they aren’t available anymore, and that their housing can fit both sides.

If you do decide to replace the EGTs, then the threads below may be of some help:
https://forum.rs246.com/viewtopic.php?t=122944

https://www.rs6.com/showthread.php/33216-How-to-change-EGT-sensors mention that RS6 and 2.7T EGTs are different with RS6 being ‘wideband’ like is mentioned in https://myaudis4.com/2014/06/07/rs6-egt-logs/

https://www.audiworld.com/forums/a6-...matic-2784251/ discusses EGT replacement on a 2.7T and that bank 1 (passenger side) is easy to change/access
Good luck!!! - Jim