To me, partner seems so much less clinical than "significant other".

Partner is good because it says nothing about gender, which is good if your partner does not conform to a gender binary, but also just if you don't want to reveal their gender either to prevent people being weirdos about it—like they often can online, especially if you say it's your "girlfriend"—or to protect yourself if, for example, you're in a same-sex relationship. But it also says nothing too specific about the status of your relationship. Are they your girlfriend? Fiancée? Wife? Something less conventional? If it's not important to the story, why not leave that detail out?

Some languages - specifically Norwegian that I know of, don't have separate words for "boyfriend" and "girlfriend". In Norwegian we have the word "kjæreste" which can be directly translated to "dearest". To me it always feels a little weird to use "boyfriend" or "girlfriend", i guess the same could be true for other non-native english speakers.

My fiancé asked me to start calling her partner because she was sick of being called girlfriend after 8 years

Because she's a woman and not a girl? (don't shoot me, im not english native. But Partnerin is the same)

Personally I (a straight person) use it in an attempt to normalize the term, so that people who want to conceal the gender of their partner have plausible deniability. If all straight people say "girlfriend/boyfriend", then anyone saying "partner" is outed as "a non-straight person trying to conceal the fact".

EDIT: but also, it connotes a deeper level of trust, support, intimacy, etc. A "girlfriend" is some chick I fool around and have some fun with; a "partner" is someone with whom I'm building a life together.

Some old nuts don't like to hear that I've been living with my girlfriend for years.

I find it interesting to hear you say this, to me, partner feels like quite a warm term. I think probably because for me, I associate the word partner with a sort of "levelling up" of a relationship, where you're not just two people dating, but two people in a partnership to help each other be the best they can be.

I do agree that it feels clunky sometimes though. I was catching up with a friend recently who paused just before the word "partner" every time. I pointed it out and we laughed at the relatable awkwardness of not feeling like you have a correct word when "girlfriend" doesn't fit. He said that partner didn't feel right either, but it was the closest he could find.

I don't recall ever hearing significant other irl, though I do sometimes see it online as SO. To me, that feels more clunky than partner.

It's fine, we're all "users" here with 0 or more "partners". Partners are second degree users who occasionally are first degree users too.

I use gender neutral terms for my partner when posting online because anyone who thinks they need to know my or their gender for our anonymous online interaction is probably someone who I would prefer not know that detail of my life.

As a bonus, I provide some safety-in-normalcy for others who would actually get treated worse were there situation known.