105 R7000 rear shifter malfunction Disclarimer: sorry for the wall of text and for my English: I tried to describe the problem as best as I could and English is not my native language.
Hello. I have a following problem with my Shimano 105 R7000 new (4k KM) rear shifter:
At the end of a ride a week ago something happened inside it and it stopped shifting altogether all of a sudden. The feeling was as if something disconnected/snapped. I took the bike to my LBS, where the cable was replaced. However, the shifting is not the same anymore. It is impossible to adjust the shifting so that both of the following work: big chainring + smallest sprocket and small chainring + biggest sprocket. The shifting is also clunky no matter what. The chain will always rub against the next sprocket before shiting to a bigger one and will often slam into smaller one. Regardless of how much I fiddle with the barrel adjuster. Also, shifting from 6 to 7 or 7 to 8 smallest sprocket requires two clicks of the lever and a downshift afterwards. Else it won't shift - the derailleur IS moving, but doesn't go enough of a distance to facilitate a shift. Most it gets is a rub on the next bigger sprocket. Conversely, shifting to smaller sprocket afterwards won't produce a shift after 1 click, but instead will shift 2 gears after two clicks (so then to back one gear I have to do the previous routine again).
Needless to say this is hell. The problem is that I had exactly all of these symptoms 8 months ago. Exact same scenario resulting in same symptoms happened to me in November when I hit first snow in Sweden. Back then, the problem got eventually solved by getting a new shifter (after lots and lots of unsuccessful troubleshooting). So now, apart from wanting to fix the problem, I really want to know what is this.
To add to the description: both times, the shiter looks and feels differently than before the incident. The lever is angled a bit more towards the frame. The braking aspect of the lever is now different as well: the distance from the lever's resting point to the &quot;max brake applied&quot; point is around 6 mm shorter. I noticed this as soon as I first got on the bike (I'm quite sensitive with my brakes).
Here are the photos where the shifter's angle as well as the brake distance capacity is visible: https://imgur.com/a/FbAF929
I think it is also worth to add that I have a new casette (2500 KM) and a relatively fresh chain (1000 KM) ridden in good weather conditions. They are both well lubed. The shifter is also lubed. The cable end bit sits correctly in the designated slot in the shifter. The rear derailleur seems to be fine too and shouldn't have been touched or affected in any way, but I have made photos as well: https://imgur.com/a/PZffPTZ
The events and symptoms you describe don't give a clear picture of what happened.

At the end of a ride a week ago something happened inside it and it stopped shifting altogether all of a sudden. The feeling was as if something disconnected/snapped.

This is consistent with a cable snapping at the head. Some past versions of Shimano STI shifters may have had a tendency to do this. Your gear and shift cables have a little round head that stops them in the lever, and the cable may have broken just below that. Presumably, your bike shop changed that cable.

The shop should have adjusted the derailer, or rather adjusted the cable tension so that the derailer shifted properly. Based on this sentence, the shop either did not do this, or something else happened to your bike in the interim:

However, the shifting is not the same anymore. It is impossible to adjust the shifting so that both of the following work: big chainring + smallest sprocket and small chainring + biggest sprocket.

Did you or the bike store adjust the limit screws? These adjust how far each derailer can travel. If you have them set too far in, the derailer may not travel far enough to shift into the specified cogs, which would reproduce these symptoms. However, you imply that you can shift into small/small and big/big, making this less likely. (NB: if the shop just replaced the cable and brought it to the right tension, they should not have touched the limit screws unless they were wrongly set to begin with.)

The shifting is also clunky no matter what. The chain will always rub against the next sprocket before shiting to a bigger one and will often slam into smaller one. Regardless of how much I fiddle with the barrel adjuster. Also, shifting from 6 to 7 or 7 to 8 smallest sprocket requires two clicks of the lever and a downshift afterwards.

These sentences are consistent with the cable tension being wrong, despite your adjusting it. If you're unable to follow the instructions for adjusting your rear derailer, have the shop do it. NB: it's not a mark of shame if you can't. Many people will pleasantly surprise themselves, but not everyone has mechanical skills, and there's no shame in not having them.
Another possible cause of poor shifting is if you dropped your bike on the side with the derailer. Novice cyclists commonly do this, as I can attest from experience. You may be surprised, but the derailer hangar (the removable piece of aluminum where your RD bolts in) can bend very easily. This is by design: in a major crash, it is meant to break before the frame takes damage; if it were a structural part of an aluminum or carbon frame, then many minor crashes or coffee shop bike spills would ruin the entire frame.
From your photos, it doesn't look like the hangar is bent. However, you have the camera angled slightly.

Last:

... both times, the shiter looks and feels differently than before the incident. The lever is angled a bit more towards the frame. The braking aspect of the lever is now different as well: the distance from the lever's resting point to the &quot;max brake applied&quot; point is around 6 mm shorter.

You said the right lever now rests closer to the bar. It sounds like someone used the reach adjustment. You can control how far the levers are away from the curve (i.e. the drop) of the bar with a little allen key under the hood. It's of immense benefit to smaller riders. This wouldn't affect the shifting by itself.
A side note for those interested: you seem to be saying that the lever travels a shorter distance before the brake pad hits the rim. On hydraulic brake levers, this phenomenon is known as setting the bite point. On those levers, you can adjust that independent of the lever reach. This is not applicable to rim brake levers, however.
Initially, I thought that your right shifter was twisted inwards on the handlebar, but I noticed that the photo is not consistent with this.

English being your first language is unlikely to be the issue. The problem is more that you're new to bikes, you don't know exactly what symptoms you are having how to describe them in technical terms, and none of us are physically present with the bike. You can try to follow the video by Park Tools. You should be able to check by eyeball if your derailer hanger is straight. If this doesn't resolve the problem, you will need to take it in to the store. Again, there is no shame in having to do this. It takes many cyclists a fair bit of fiddling to understand how our derailers adjust. Until I understood that process, I was essentially turning screws and cable adjusters without any clear purpose.