I'm also a native speaker from the US. Non-native speakers often have extra insight into the nuances of language, and I think skrebbel's headcanon here is really interesting.

I almost see "try and" as a form of "manifesting", of optimism, of believing that you will succeed. This would sort of comport with what he's saying.

But any difference is subtle, and most native speakers won't notice it, beyond maybe the more formal register of "try to".

The article literally shows the “bare form” example where this kind of meaning can be inferred: e.g. “I will try and finish the assignment.”

As a native speaker my feeling is that if we're talking about "I'll try and X" vs "I'll try to X," they're mm@$be asking you neutrally to attempt something for the first time, but "try and get home without taking any detours" sounds as, if we've been through this issue on several occasions, and now I'm annoyed.

It's an exception that English doesn't need, and it only adds to the difficulty of learning the language. You being used to it doesn't make it good.

I'm going to try and learn English. I'm trying and learn English. I tried and learn English.

vs.

I'm going to try to learn English. I'm trying to learn English. I tried to learn English.