What does it mean for a prospective ger to feel they have a "Jewish soul". I understand that wanting to search, love and search G-d is something gentiles can do... can it really come down to feeling like observing mitzvot (and being bound to do so) makes us closer to Him? I don't take Judaism lightly, and I'm not implying mitzvot are simple, but is this an example of what people refer to as a Jewish soul?
This is actually a brilliant question and I've thought about this a lot since I received this ask. Definitely led me to a lot of reading over Shabbat.
So, the Kabbalistic interpretation (I am not a Kabbalah expert, and you should be suspicious of anyone who claims to be, there are very few) is essentially that a soul is created every time a husband and wife have relations. The soul either comes down to become a human or it stays in heaven. For Avraham and Sarah, they tried many times but Sarah was barren for many years. It is said that the souls they created stayed in heaven, and these are the souls that have been put in converts. This is why they're called sons and daughters of Avraham and Sarah, they are directly from them.
Speaking from those I know who have converted, their paths TO judaism are all unique, but what binds them all is a deep, intense, unwavering, life-long connection to Judaism and the Jewish people. Some converted later in life after growing up in Jewish communities, some converted later after meeting a Jew for the first time, discovering more about their people, and feeling instantly connected. Most have faced intensely painful hardships and rejection from friend and family for their choice to convert to Judaism, but all have said they would make the same choice, because their soul feels at peace, it feels at home. Their neshama is with its mishpacha.
The conversion process is long and difficult, and it's designed to be that way for many reasons. Mainly, it is to weed out those who don't have this Jewish neshama, and keep those who are dedicated and sincere. It is a life long commitment, once you convert you cannot go back.
I have only ever met one person in my lifetime who converted and regretted it. She converted when she was in her late 20s, and the process only took about a year for her type of conversion. She's still active in the community, married a jew and has jewish children. But once I stayed up with her late one night and she confessed to me that she wished she had chosen another faith because Judaism is very demanding, and she never understood what people meant when they described the feeling of a jewish soul. She expressed that while she loved her family, if she could do it over she would have converted to another faith that called her more.
I feel for her. She is saddled with all of the mitzvot and she does them because now she is required and her husband does them too, but she wishes she did something different in her younger years. This is incredibly rare though, most converts who have gone through the process never express regret. But it's rare because the process is meant to be long and difficult. We don't want to bind you to mitzvot you no longer want to do.