What potential issues with copyright are there from offering (paid) access to this tool to run on sources including Youtube, and with the output containing the source audio?
You could have asked the same question when Google started building their index. Or OpenAI trained their models.
I'm in Germany. I'm a licensed lawyer. I see the dangers.
The safest path will be to simply offer the production of multi language translations to content owners themselves. Which is also going to be more efficient - translating the thing at the source, rather than having consumers each create their own translation.
But the original intent for this has been to have my computer translate a video I want to watch with my kids in my private home. Technically, it's not "my computer" in the sense of being just the device that's physically in my home. There's stuff that happens in the cloud. Technically, copies are being made. So one could argue the point.
For most people today, getting your content seen and consumed is the highest you can achieve. To sue someone from another country who cares enough to pay someone else to translate it for him would seem bonkers. But I'm sure there are lawyers who are desperate for work. Who cannot code, and can't be bothered to learn, but still want to do something "in AI". I'll at least give them a hard time. And dare they use ChatGPT hallucinated references on me! :)
You're creating a derived work, so you would be violating someone's IP unless the licence is permissive, and making money of it. That usually attracts the attention of whoever owns the IP.
Who's "you"? I'm obviously not a lawyer, but instinct tells me that end users are the ones creating a derived work by uploading a video they may or may not have the right to distribute. Linked website is just a tool, perhaps a cloud-based one, but still just a tool.