Acting like 6 months away is a big deal when they pretty much had a relationship consisting of line messages and a couple meals for a year after graduation.
Additionally, flights from Japan to Germany exist.
I've always wondered, is study abroad so common in Japan as it appears to be in manga/anime? Or is it just a dramatic trope?
Its not just Japan. There are foreign exchange programs in just about every college in the US.
For highschool and younger students, the struggle is very real (if not super common) because Japanese companies will sent employees to the US and other foreign countries for years at a time so the choice is "leave Japan with dad or don't see each other for 2-5+ years". Nissan near where I lived had what ammounted an ex-pat village and integration help for employee's children - they put trained councilors in the local schools to help deal with the Japanese students when they inevitably had a melt down due to homesickness or culture shock.
the reason parents did this goes into:
For College,
Its very common in Asian countries because to try to keep this short:
The US college accreditation program (which foreign schools can qualify for) is an international gold standard. A degree from a US accredited school is good world-wide, while degrees from schools without an accreditation are nearly worthless outside of the country in which they were earned.
Additionally, while not relevant to this manga, completing a foreign program looks good on a Japanese resume. Most Japanese companies have braches in foreign countries and "Proven ablity to live outside Japan, be functional, and not completely lose your mind" is a big leg up on applications. (Nissan had a number of people it sent over just absolutely fail to adapt to the US and return home.)
Basically, college kids want to experience the world and an easy pitch to asian parents because of the very real benefits it brings.