I am going to try that, but from what I observed from watching the flow dynamics calibration at the start of the print, it came out very straight and in constant strength - also, I tried different nozzles, which all led to the same results - does not seem clogged 
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I am currently doing a test run, when it is finished, I will try cutting it quickly to see if it keeps oozing / stringing. When changing filaments, I observed it kind of does - but the algorithm of the A1 heats up to 250°C when loading, so I am not surprised it keeps leaking since this is way too hot for the PLA I use.
I would be VERY happy if it was just a filament issue - but in that case, would it not get better at lower temperatures that cause less ooze creeping out? However, at low temps it is the same, the folded part is just more solid.
Also, it does not really explain why I all of a sudden got this on all filament (including new ones) when before this did not even happen with unprotected PETG (especially the skirt line).
Will give it a try later - maybe the open filaments caught moisture and BOTH the new ones were not properly factory dried. That would be quite an insane coincidence, but hey - you never know .
I will update once I tried, also hoping this helps others who are facing the same issue (saw thread on reddit etc. of people also having comparable issues that never got resolved).
Also: I manually adjusted Z-Offset from 0.02 to 0.03, so far it looks A BIT better, but may be coincidence.
UPDATE: The print with 0.3 mm Z-Offset actually went way better, though there are still pieces of debris, but no holes in the bottom layer - maybe that might have something to do with the issue?
Also did the extrusion test - it comes out in a very solid line, but after cutting or pulling, it oozes a lot at 220°C. I tested at lower temps and the temperature it finally stopped oozing after the extruder stopped was at 185°C.
What is still not explained by this: Oozing filament would explain extra material applied that does not belong - kind of like a blob at the start. However, this should be impacted by lower temperatures. In my case, it does not put a blob at the start putting MORE material than required - instead, it puts the right amount of material on the plate but folded / extruded at the wrong time, which leads to blank spots, followed by folded material.
UPDATE 2: This may have solved the issue!
So, running out of ideas, I switched back to the 0.4 mm nozzle and (even though I don’t want to jinx it…) the first test with the very same “maybe wet” filament turned out SO MUCH better. Skirtline closed nicely, also, no debrist / not completely molten filement in the wall lines etc.
There ARE still some very minor blobs at the start of some of the lines, especially when the travel distance between two squares is rather high, but I can definitely see that this may just be from the slightly prolonged time the filament stays in the nozzle and gets a bit softer than it would - this is probably just physics in the end and this is the part of the problem that made sense to me in the first place. Things that did not make sense like the shortened lines with shortened filament (after long travel with longer time inside the heated nozzle, the opposite should be the case - as it is now!) are currently gone.
So, what happened (probably)? I think I changed too many parameters at the same time.
I started to see issues with the first layer, so I initially thought the nozzle / hotend was jammed, so I switched to a 0.6 nozzle (the spare 0.4 nozzle is ordered but due to the holidays, it is taking a bit longer than usual). If a jam would have been the cause, that would certainly have made a difference, however, it didn’t.
After that, I tightened all the 7 screws (3 front + 4 back) on the pressure block - one of the 4 screws on the back was indeed slightly loose, maybe half a turn from sitting snug, honestly, I cannot say how big the effect of that was.
From that point on, I did not change anything regarding the nozzle (except for deep cleaning the whole extruder) but I got the issues described above.
Since nothing else helped, I wanted to try the 0.4 nozzle again and switched + recalibrated and tried the same model again (same filament, same setting) - and so far it looks near perfect.
As mentioned, there are some slightly bigger starts of the line after travel, but no material is missing → This is fine for me since it makes sense. Also, these mini blobs get covered perfectly by the next layers. There are some TINY pieces of debris / blobs that happen in seemingly random places (almost unnoticeable), but this is something that I can ABSOLUTELY attribute to filament that is not dried perfectly → also explainable.
However, I checked what other users experienced with the 0.6 nozzle profile - and indeed they had some problems (retraction settings etc.).
So, what I think has happened:
→ Issues with 0.4 nozzle (probably loose screw) → change to 0.6 nozzle, even worse (same problems + new ones apparently specific to 0.6 nozzle) → screws tightened (maybe improved things, but the 0.6 specific issues remained and I was focused on them) → (many other tests) → change back to 0.4 nozzle → Everything is fine, since the 0.6 specific issues to not apply and I probably fixed the initial problem by tightening the screws.
That screw issue also explains why it got worse over time without changing any parameters - and the 0.6 specific setting problems explain why the actual fix did not show any effect (if I had started with a 0.6 nozzle right out of the box when everything was still tight, it probably would not have worked as well). I guess it is always bad if you get two rather similar problems from different sources at the same time and start focussing on the wrong one.
This is the first print after changing back:
Now, I will keep my fingers crossed that it stays this way 
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THANK you to anyone who tried to help me with this (and bothered to reach this “novel” )! It was a bumpy start with the printer, but I guess it helped me a lot with further understanding and troubleshooting, so I try to see the upsides.
I will set this to “solved” for now but keep posting updates if something should change again.