Right. I still have to guess as it could be a TDI 90, 110, or 130, however I expect the SE level of fit to be with a TDI 110, like mine.
Limp mode doesn't always trip an EML. On the other hand, does your EML come on during the pre-start check, when you first turn the key? All the warning lights should light up for a second or two so you can check that they are not broken.
The most likely cause, though, is stuck turbo vanes due to the turbine section getting sooted up. The best fix is to remove the turbo, disassemble and clean it. but it's not for the faint-hearted. Lots of work under the car, and being in the exhaust assembly, bet on all the bolts being seized, have replacements ready: even then, you stand a chance of breaking one, which is a real pain.
Alternatives to disassembly include the "Italian tune-up" - yes this is one time when ragging the engine can
help (within limits). The soot is generated by the action of the EGR valve during part-throttle openings, and if you don't get the engine loaded so the exhaust gets hot, it doesn't get burned off.
You want to get the turbo hot and keep it hot for a good few minutes. Best option is to find the steepest bit of motorway near you, load the car up and drive up it one or more times as fast as you think is wise (without flooring the throttle - which generates more smoke).
Putting some fuel treatment in the tank can also
help - the general opinion of this forum seems to favour Millers.