You might be able to get your clients to sign something to allow usage, but if you don't, as you say, it doesn't seem wise to vibe code for them. For two reasons:
1. A typical contract transfers the rights to the work. The ownership of AI generated code is legally a wee bit disputed. If you modify and refactor generated code heavily it's probably fine, but if you just accept AI generated code en masse, making your client think that you wrote it and it is therefore their copyright, that seems dangerous.
2. A typical contract or NDA also contains non disclosure, i.e. you can't share confidential information, e.g. code (including code you _just_ wrote, due to #1) with external parties or the general public willy nilly. Whether any terms of service assurances from OpenAI or Anthropic that your model inputs and outputs will probably not be used for training are legally sufficient, I have doubts.
IANAL, and _perhaps_ I'm wrong about one or both of these, in one or more countries, but by and large I'd say the risk is not worth the benefit.
I mostly use third party LLMs like I would StackOverflow: Don't post company code there verbatim, make an isolated example. And also don't paste from SO verbatim. I tried other ways of using LLMs for programming a few times in personal projects and can't say I worry about lower productivity with these limitations. YMMV.
(All this also generally goes for employees with typical employment contracts: It's probably a contract violation.)