Can foreigners also move to spacious homes in Seoul?

Hello! I'm a foreigner who has been in Korea for 3 months now. I am currently working at an academy in Gangnam and living in a studio provided by my workplace. However, I want to adopt a dog and move to a bigger place. My predecessor has been here for 6 years and the location is really great, just a 2-minute walk to the school. But my dream is to have a life with a dog, so I need a bigger space. Does anyone have a similar experience? I'm wondering how to move out from the academy-provided housing. Should I go to a real estate agent, or should I talk to the academy first? I've tried using the Zigbang app and visited a few real estate agencies, but they say the deposit is high for foreigners. 😢 Can you please advise me on how to approach this situation? I would really appreciate it if you could share your experiences!