Yes, there are 3 sensors around the DPF - two Exhaust Gas Temperature sensors (one before and one after the DPF), and a Lambda (oxygen) sensor. To be fair, if it was any of these three sensors they were trying to remove then using some heat to do so is viable because those sensors live their whole lives at some seriously hot temperatures and can handle that sort of heat abuse. The wires going into them are very well shielded so they can also cope with hot temperatures. There is also some Differential Pressure Sensors on the end of pipes that come off of the DPF (so not directly attached to the exhaust system / DPF) but the
garage were probably talking about the former 3 sensors.
The light you have on is the "Emission Control System" (ECS) warning lamp. The ECS light and EML (Engine Management Light) are one and the same thing. There are a whole host of sensors that could cause that light to come on, not just the 3 sensors around the DPF that the
garage were focusing on, so if they couldn't read the actual fault codes of the car because of an "unknown error" then they shouldn't have just started playing guessing games at your expense.
The term "deep clean" can only mean regeneration. They probably just said "deep clean" because they didn't want to baffle you with any technical jargon. However, with just the ECS light on and no DPF light, there was no need to do a regeneration of the DPF because there was no fault light indicating that actually needed to be done so they shouldn't have done that as part of their trial and error exercise at the price they were charging to do it.
I don't know where you're based but I would be inclined to try and find a friendly forum member nearby with VCDS and get them to do a fault code scan of your car. The
garage are clearly trying to use some incompatible diagnostics software. I assume they're not a VAG
dealer or independent VAG specialist? (I would certainly hope not based on your experience).