So let's see if I can answer all of your questions!
"I'm wondering what Si does for you?"
- As you may already know, Si is about making references to the past...so we rarely ever forget. Everything that happens, we tend to remember as if it just happened yesterday. Since we are dominant Si, we make most if not all of our decisions based on the past, on experiences. So with my Si, I tend to make many decisions based on past experiences, and I also get to remember many events in great detail.
"Does it make you sentimental as it would an esfj, or does it make you earthy and "one" with the material world like an estp?"
- I'm not so sure. Because do recall that Si is also shared with ISTJ. They have Si dominant but Te secondary. I'm not sure if Si makes us more sentimental, but again, our decisions are made strongly from past experiences and that overtakes our feelings sometimes. As for being earthy and "one" with the material world, I'm also not so sure. We tend to have this kind of focused expression when we are thinking...we do not exactly pay so much attention to the external world as Se dominants do, but when we focus, that's when we notice the details. Other than that, our focus tends to be on our past...we just think about past things or whatever happens to be on our mind at the moment. We are somewhat similar to INFJ, who have that Ni as their primary, and tend to have an expression that they are drifting off into space. In ISFJ case, we do too...but we are thinking about past things....usually at least.
"Okay, so would you say your Si is more like a pantry or a thermometer?"
Well...in a sense yeah, our Si is like a pantry. We keep all these memories and experiences within ourselves and remember them so we can infer on them to make current or future decisions. It's pretty neat.
"But it seems like isfj Si is..kind of like a point of reference or something?"
- In a sense yes. It's used to make decisions in the future, by looking at the past. Difference with ESFJ is that I guess your Si is influenced a bit by your dominant Fe, making things a bit more personal and sentimental, while our Si doesn't necessarily have to be sentimental. We have many points of references, it's our entire life that has all those reference points
I really hope all this helped you!