I've started it and really liked what I've read, but I wanted to be in a different headspace for it, so I've put it on hold for now. It felt ahead of even current times tbh.

It's less me being embarrassed in regards to my "reputation," and more about me being embarrassed to say it's worth reading. Like, some of them are really pervy or have super disturbing implications, but there's other stuff that I feel they do really well. I guess it's more that I can't uncritically recommend them without a whole lot of disclaimers

I mostly read manga, so my suggestions might be of limited use if you want anime. I think Onimai is a fairly trans code genderswap story, and while it does get a little gross sometimes, it hasn't completely alienated me yet (it also has an anime adaptation). Until I (M) Become Me (F) is fairly mature in how it handles the subject of gender, and isn't really pervy at all despite occasional nudity. Kare to Kanojo no Sentaku handles gender well enough, but if you go in expecting the obvious romance, you will be disappointed. TS Gakuen no Nichijou was surprisingly good and didn't cross the line with its pervertedness like some others do. I'm a High School Boy, but I Got Gender-Swapped into a Gyaru is super perverted, but somehow even more of an egg story than Onimai. Zenbu Kimi no Sei is also quiet good, featuring both nonbinary and explicitly trans characters.

There's also more grounded stories with more realistic gender bending that probably deserve a mention. Kakumei no Hi, is technically about an intersex person, but the character goes through a gender transition and has to deal with a gang of chasers literal chasers. Senpai wa Otokonoko challenges understandings of sexuality and gender by the main character simply choosing to exist. Sakura-chan to Amane-kun is a cute t4t story that will probably never get finished. Love Me for Who I Am is refreshing in how it refuses to tip toe around LGBTQ issues like most other manga (Shimanami Tasogare it's similar, but not focused on gender). I Cross-Dressed for the IRL Meetup Is also explicit trans rep, but still worth mentioning.

There are other stories like Kashimashi: Girl Meets Girl and I Love Yuri and I Got Bodyswapped With a Fujoshi! which I haven't finished and can't fully recommend. There's also plenty of stories that while interesting, I can't really recommend for one reason or another.

I assume they mean slice of life?

Ones that take place in an everyday "normal" world that's mostly similar to our own rather than fantasy or sci-fi. There's usually some fantasy or unrealistic science involved in the genderswap, but the setting is otherwise exactly like our own.

There is some good shit on scribblehub, but I'm big on urban fantasy and so much of the genderbending is that. As far as eggy authors are concerned, I try to avoid such speculation, even when the signs are billboards. If they want to come out, they will.