적응하다 (verb) = actively adapt oneself to fit in to a new environment or cope with a situation. 익숙하다 (adjective) = be comfortable because of familiarity, like an old hat. So if you transfer to a new school or join a new company, you try to fit in and get used to the new setting: 새로운 학교에 적응하고 있다 / 새 직장/업무에 적응하려고 노력한다. After you spend some time at the new place, you now know the people well and feel comfortable - i.e. you have become accustomed to the new environment: 새 학교/직장에 익숙해졌다.

Hello, this web page is useful: https://wiseinit.com/%EC%A0%81%EC%9D%91%ED%95%98%EB%8B%A4-%EC%9D%B5%EC%88%99%ED%95%98%EB%8B%A4-korean-words-vs-words-s2-7/ The writer mentioned this: 적응 is to begin adjusting and 익숙 is to finish adjusting.