Heyoo! I would love some recs where the main character ends up in a new world, alternative world, time travel or something similar. Thank you in advance :D

I'd actually highly recommend you to check out Along with the God: The Two World . This is a movie with multiple sequels however you don't have to watch all to have closure or understand the story. It fits what you look for => alternative world / new world. It is really really good  

For dramas:
ending up in the past:
Mr Queen
Moon Lovers: Scarlet Heart Ryeo
Life on Mars
Tomorrow with you
Someday or One Day
365 Days: Repeat the Year

Parallel world:
Welcome 2 Life
The King: Eternal Monarch

Character ends up in another world/another side of the world:
The Legend of the blue Sea - she kinda always lived in the world but she is a mermaid and hasn't lived in the human world "today" world.
Hotel del Luna - character gets introduced to a new side of the human world
Mystic Pop Up bar - character gets introduced to a new side of the human world
Missing: The Other Side (season 1 and 2) - character ends up in another world
Witch's Diner - character is introduced to a new side of the world
Angel's Last Mission - character is introduced to a new side of the world
Tale of the Nine-Tailed - character is introduced to a new side of the world

I'm a few episodes into My Perfect Stranger. A TV news anchor finds a car labelled Time Machine, with instruction manual. Seemingly it only goes into an old tunnel and through to a nearby town.  He goes back to 1987 to investigate a serial murder case, getting himself hired as a high school teacher because all the suspects were teenage boys.  In one of his trips back and forth, he accidentally picks up a second person, a young woman who has just lost her mother, also a teen during that time.

(It occurs to me that I have absolutely no idea why he doesn't journey further.)

The Story Of Park's Marriage Contract - Joseon era new bride's husband dies on her wedding night (he was in poor health). Soon after, she is kidnapped and thrown down a well, emerges in the present day in a hotel swimming pool saved by a man who looks like her deceased husband. The fish-out-of-water aspect was fun.

Parallel World (China 2023, does not seem to be on above lists). Rather than a parallel world, I'd describe it as a pocket world that some people can drive in and out of. Really good actioner with strong fantasy elements, superb performance by the FL.

Paripi Koumei is about famous strategist Zhuge Liang transported to 21st century Japan. It's such a fun drama, imo

Someone mentioned the Taiwanese version of this show already [Someday or One Day] but I truly recommend the Korean one, A Time Called You. 

It somewhat hits what you've described - the MC doesn't time travel to her own body, but someone else's, and attempts to change the past while changing the future, and there's a very interesting butterfly effect explored here. 

Others I would recommend in the time-traveling genre...

- Something For One Thing 

- Hit The Top [The character time travels to the future instead of the past]. 

- Marry My Husband is a now-airing or just-finishing-airing drama that's based on a popular webtoon or webcomic about an MC who dies, and wakes up in her past and vows to change her future.

I have a list for this: Transmigration: Out of place/time/body 

Hope you find some new suggestions on there!

Lost Romance Fl falls into the book world. Full-length episodes pick up really after 1st episode.

Likhit Haeng Jan Fl a girl from the past change places. Full-length episodes.

Live up to your name Ml is a doctor from the past that time travels to the present. Full-length episodes.

Love Destiny Fl goes into the body of a villainous woman in the past. Full-length episodes.

Love for Loves Sake Ml enters book. Full-length episodes. BL

I recommend you joy of life

If you're OK with BL:

Another I would recommend, but only if you have seen Season 1 is "Tale of the Nine-Tailed 1938" (South Korea, 2023)

There is also a crime drama where two detectives talk across time: "Signal" (South Korea, 2016). China, Japan, and Thailand also did remakes.