How can I make my language skills stand out if I don’t have visa sponsorship (yet)?

I’m currently job hunting in Korea on a D-10 visa. I've got TOPIK level 5 and some experience in Korean-English interpretation, but I’ve noticed that a lot of companies seem to prefer candidates who already have a visa. In your experience, how much do Korean language skills actually help when you're still looking for visa sponsorship? And is there any way to make strong language skills stand out more, even if you don’t have a visa yet? Any tips or strategies would be super appreciated, thanks in advance! 🙏