Congrats on switching from a major you didn't like to one that you do. Though you did not finish the biology major, I think you should view your background in science as an asset. You have a cross disciplinary perspective that is rare I think. From reading your post, I wanted to say that I think your next step should be to try to get out of your own head a little. You're a smart person, you're doing well at university with a wide array of interests. You're clearly looking to get better at being a historian and to put in the work to do so. That's really all you can do. So concentrate on getting the readings done for class, participating in the conversations based on the reading, and pursuing primary source research. Maybe go to your professors' office hours with specific questions from the readings or from class; this can be a way to show you're interested, but it might also let you have conversations with your professors and develop those relationships. You might also talk with your profs and explain your unique position. "Hey, I was wondering if we could set up a time to video chat during a time that is convenient for you. I recently switched to a history major from biology. I'm really loving my new major. I'm interested in East Asia, specifically blah blah blah (time period, subject matter). I'm wondering if you had any suggestions for how I can improve blah blah blah (in class, on papers, with my research, etc.). I'm also looking for topics that might make good future research projects." Etc. Office hours aren't really for people to come and hang out, but if you have real questions and you show you're interested, most reasonable, kind professors will love working with you.

If you want to pursue an advanced degree in history, you should prioritize learning a language. Are you in the US? Maybe look into the Foreign Language and Area Studies grants, which supports language acquisition for lesser-learned languages like Mandarin. You might also be able to find language learning opportunities in Taiwan. I know a lot of my history major peers took some time off between undergraduate university to travel, each English abroad, work other jobs. Perhaps there is some sort of internship or something. Perhaps your school has a study abroad office or career development office that could help you search for those things. Since many East Asian languages are in demand, you might even be able to find community night classes for a language. Language learning is difficult of course, but it boils down to practice and a willingness to make mistakes/embarrass yourself as you are learning, like most new skills. Human brains are made to learn multiple languages. You can do it!

If you decide to apply, you will also need a quality writing sample. This should involve primary source research. I recommend working hard to write a good 15 to 25 page paper in the last few years of university that shows your research abilities. I think it is fine to use translated sources for this and then say on the application somewhere, "since I wrote this paper, I have undertaken the study of foreign languages. I am now prepared to do research in a different language."

Lastly, I'll just say that many people would love to be professors and begin the processes to do it, but then for one reason or another they end up on a different path. That's totally fine and totally normal! Finding a job as a history major is hard because there isn't a set career path, but you develop an important skill set that if you market correctly while you're looking for jobs, will make you a very competitive candidate. Like all career development, it's all about networking. Building connections, trying new things, learning foreign languages, and getting better at reading, research, and writing are all things that will help you network and will help you find a job, even if you end up not teaching at a university.

edit: typo