I always find MN threads on languages confusing.
There is a big difference between studying a language and language acquisition. And it is far easier to work in a language if it relates to an area you already know. So chemistry in Spanish will be easier if you already know a lot of chemistry.
I have worked with people from all over the world. Many had several languages, and most, given they were working in English, were bilingual. The standard tip is that if you want to learn a language, is to use it. I went to work in Germany without German but made an effort first to watch a lot of TV (new is good as the same topic will roll over several days so you get used to the vocab). Sesame Strasse was my go to, and I also chose to share a flat with Germans, took regular classes. I would also inch my way through magazine articles, jotting down new words and revising them.
A later employer saw language acquisition as part of the job, nothing special. Three months intensive from one of those executive language schools was seen as sufficient for most Western European languages. I covered a maternity leave in Paris so had to make do with two. Not easy to start with but by the end of six months there, and despite the office language being English, I was fine. I was so rubbish at languages at school I was tempted to find my old French teacher to tell her I had gone on to acquire four languages.
Taking a degree overseas will be different in that you would have to write in the language. (When I worked in Germany, sensible bosses would have English mother tongue secretaries to even out their drafts.) Less of a problem with STEM degrees than humanities.
Having a language is increasingly important. When DS finished his PhD and was looking for an academic job he was limited to English speaking countries. Almost all of his peers were able to consider positions using both their mother tongue and English. I am a landlord and currently have a Polish tenant who is on a graduate training scheme at a very well known investment bank. He took a Masters at LSE and speaks Polish, German, French and perhaps other languages. (He rather cleverly is sharing with a Frenchman and they converse in French.) It seems obvious that employers will be prefer him to a monolingual Brit with a similar academic background, even before the EU passport comes into play.
My advice, based on what I have observed is that if you are aiming for an international career, is to take the plunge, leave your comfort zone and do some study overseas. Take a year out if you need to or spend the summer as a au pair. Exposure is key. Whether it is a whole degree, or a year, will depend on the status of the institution. I would also suggest that it is better to study something other than languages, or perhaps a joint degree, unless you have a strong interest in language, literature and culture. Simply being overseas, and making the effort to interact with locals, will give you plenty.