I only use Indeed.com so that my info is only siphoned from one place. I feel like they have good listings and they have options to hide some of your info from employers and random observers. Avoid linkedin at all costs, having a profile has gotten me zero benefits and it is an extreme pain deleting your account.

You can also take steps to protect your contact info, specifically your email/phone/address. I only put the city I'm from on my resume and you can use email masks or alts like firefox relay or protonmail plus, or just make a separate email only for work. For phone numbers I use JMP.chat to give me a second number to use solely for work and Indeed.

In the end a lot of your work info is gonna be pseudo-public, because you do need to convince prospective employers of who you are, but you can control the sphere of that information to keep it confined. Imo, having a stable job is worth that trade; you don't have to do a deep dive into your personality or personal life to get a job. Just enough to be convincing