Visibility works differently depending on which side of the marketplace you're on.
If you're a job seeker
Your resume and contact details stay private by default. They're shared only when:
You apply to a specific job, then that employer sees your application.
You switch on "open to work" visibility, which lets employers on a plan with talent search find and view your profile before you apply anywhere.
You control that toggle from your profile at all times.
If you're an employer
Your business page and open jobs are public once posted, that's how candidates find you in the first place. Applicant details, though, are only ever visible to your own team, never to other businesses or the public.
Want your company page offline? An owner can hide the public business page anytime from My business → Overview. It takes the company profile out of search and shows visitors a "not found" page, while you and your team still see it and your individual job links keep working. It's a lighter step than pausing the whole business.