To reply to your question "is it okay to replace 8K0 413 037/038 K with 8K0 413 037/038 L, I have checked an online parts listing that I use and trust when buying parts from VAG dealerships, and yes, the "K" version has vanished and "L" is the current versions for these cars.
One question for you, I noticed from looking at your pictures, that you used a very short spring compressor - which brand is that? I'm curious as I'm working on the front suspension of my 2011 S4 and when I went to compress the springs to change the top mounts and shim/thrust washer, I found that both my spring compressors, different types fouled the alloy top plate - so, I bought a pack of 50 M16 plain washers, M16 X 30 X 3, and used them at the other end of the spring compressors to "take up" the slack - that worked perfectly!
These cars can be quite challenging to work on the front suspension, I'm replacing all the front arms, but also felt the need to replace the top mounts as I'm hearing/feeling a slight noise when I encounter an unseen deep ridge or pothole that was not happening when this car was younger. I've now put that down to the bonded bush where the strut fork connects to the front lower front arms having aged - hardened and maybe compacted. Plus I had a "thing" about this car being built when M12 ball joints were fitted to the front lower front arm, so I'm also using that as an excuse to replace the ball joint and arm for the later M14 version. The other issue that I had was, when I drove it out of the garage for its MOT in late January this year, it logged an ABS wheel sensor fault, I quickly checked it with VCDS and found that it was the front RHS sensor, checked it impedance with a meter and found that it was shorted out! Due to time limitations etc plus any other "it is very cold" excuses, I just got the MOT garage to replace that ABS sensor. After discussing this on another VAG forum, ie I asked the question "why or what causes an ABS sensor to go short circuit?" I was advised that it could be due to a build up of corrosion on the rear face area of the wheel bearing! So, soon after putting some fault free miles on this car, I removed this newly fitted ABS sensor - a Bosch one that I had supplied to be fitted to that car, and discovered that the face of the sensor finger nearest the wheel bearing has now got score marks on it - so putting 2 and 2 together I'm thinking that this new ABS sensor will have a limited life span, so I really need to correct that while I'm replacing the suspension. So I ordered in a new hub/bearing assembly - an SKF branded one.
Moving forward maybe 6 months, I've finally got round to starting to correct all these issues with my 2011 S4, first plan was to remove the top and bottom pinch bolts as they seem to be the worst part of the job. RHS bottom pinch I eventually got out after forming bunds around the exposed threaded end and the pinch area and filling them with PB Blaster and leaving for a few days, then after working on that bottom pinch bolt a lot I used an induction heater on it a few times, still not budging, used a gas torch on it, ie just MAP gas, eventually it could be removed, top pinch bolt same treatment plus lots of action from an air hammer - no luck! Moved to the LHS, same processes, the lower pinch bolt eventually started to move so I worked away at it - then realised that it was not unscrewing - it had quietly snapped at the end of the threaded section!! So now big trouble, I drill a pilot hole then opened it up but could not reach far enough in to pass through the snapped end which is in the pinch area! So, I cut up the old snapped off pinch hole and drilled a pilot hole down through its head and fitted that back into the lower end of the knuckle, and used that as a guide to drill a pilot hole into the other end of the snapped off bolt section using a very long drill bit, that failed miserably as the resulting new pilot hole ended up entering the snapped off bolt part at an angle and then the drill tip broke off when it encountered the first hole that I had drilled from the outer end! So now I've got a damaged knuckle as the drill has moved across into the alloy! No chance to use extractor on it, game over for now! So now in a state of more than slight annoyance, and with already bought a lot of parts, I just thought, buggar this, and placed an order for 2 new knuckles from Audi - and another new SKF hub/bearing assembly etc. The LHS knuckle was not available, ie on back order from the supplier, so that placed another delay on this job, maybe another 10 days. So now I've got most of the new parts on the LHS, I also found while cleaning up the brake splash guards that they were badly perforated at 2 of the 4 fixing holes, so I bought a pair of new ones - oh, and I had noticed that there had been a slight bit of "wobble" coming from the brake pedal, and a bit of runout on the RHS brake disc, so I had already bought new discs, pad set and new guides kit!
All in all quite a lot more work and time and money than I had expected to be putting into this car.
PS, if anyone needs to remove the front brake splash guards from a car with Cobapress front knuckles, make sure that you are aware that one of the fixing screw hole is a through hole, and that that bolt will been seized not just a bit tight to remove - I only discovered that after I had snapped that bolt, knowing this I used PB Blaster on that same bolt on the other side and got it out intact.
Hopefully I'll find that taking the RHS top plate bolts out will easier after reading about your experience!