Well, when you say "logical analysis", "reasoning", "hard formulas", what I think of is Ti. There's a bit of Si e.g. focusing on past behaviour, sensory things, but more the Ti.
About social anxiety... I'm not sure how social anxiety ties into the functions precisely, but I can say as an INFJ that I have pretty bad social anxiety. If you ask me which causes me more anxiety: people or logic? I would easily say people. I think people can be just... anxiety provoking, idk.
But here's some evidence that Si causes you anxiety too:
In your signature it says "I don't think it's so personal Anymore / I don't think it's irreversible Anymore". To me that is an elegant description of overcoming the difficulties associated with Fe (personal) and Si (irreversible). I can say as someone who has Si in the 8th position, that Si causes me a lot of anxiety, and the concept of "irreversible" seems tied into that anxiety. For me though it's having a bad reaction to being reminded of the past. A memory will come to my mind, and it won't necessarily be a bad memory, but it will cause me anxiety just being reminded of it. Whether I made a mistake or something bad happened in the memory or not, I will feel that I/it did.
Regarding people as blank noise... I think that's more of a low-Feeling trait than social anxiety. But I think it's consistent with Fe being in the tertiary. The tertiary is perhaps the most neutral function, in that we kinda identify with it but not strongly, kinda want to distance ourself from it but not strongly. I suppose I can be like that with logical analysis. I tend to be quite logical, but if it becomes the focus I just don't care. I can do it but I don't necessarily like doing it unless I have a specific interest in the issue being analysed. Whereas with something Se related like sports, while I can sometimes enjoy that, I am usually very reluctant to engage with the physical world. I for the most part just don't like sports, or physical challenges or the like. Being made to react in the moment to incoming data is generally anxiety provoking, which is one reason I can socialise online but often not in person, because online is less "real time".
Regarding approaches to learning, I don't know enough about the example you provided to say what's going on there, but I associate Si with rote-learning. Si is the most capable of taking in a large amount of data and processing that data for regularities, so they are good in subjects where there is a lot of information to take in as opposed to subjects where the theory is paramount. From what I understand chemistry can be approached from either a factual or a theoretical angle, and it probably does depend on the kind of chemistry as to which is more likely to be appropriate - though I suspect that both would need to be incorporated to really excel.
I guess questions to think about regarding Si...
Do you like / are you good at rote learning?
Do you like / are you good at repetitive tasks?
Are you someone with good "attention to detail"?
How do you feel about looking back at the past?
That's all I can think of for now.