Lakewhut, it’s not true that chasidim influenced the world to abandon non-glatt. That was a decision made by American gedolim, rosh verishon rav Moshe, who was, last i checked, not chasidishe.
It is correct, though, that “chasidishe shechitah,” along with non-gebrukts products and other chasidishe minhagim have become pretty standard. It’s important to remember, however, that there’s a reason most Brooklyn shuls are nusach sfard – I don’t think it’s inaccurate to say that most frum ashkenazi jews in the NYC area oday have some chasidishe roots.
Re, chasidus/nefesh hachaim – one can say that the nefesh hachaim teaches chasidus, insofar as chasidus is defined as toras hanistar taught as a part of avodas Hashem.