Unfortunately, having a job is horrible for your privacy. You’re required to provide full personal details to be hired to an employer with dubious security who forces you to sign up for accounts with likely either Microsoft or Google. Depending on your position you either need to use your personal phone for work (and your work accounts are easily tied to your phone), or carry a work phone with you, which you have even less control over than normal.
That isn’t really helpful.
I think to your original question, it’s more about sanitizing what is published. On LinkedIn and Indeed. Whenever possible apply directly through the website. But everywhere is going to require similar levels of personal information. As far as being worried about spam; using another email account is probably easiest. You don’t want to risk missing an important email while you are looking.
Wow, one more thing to thank Reagan for that I was unaware of. Thank you for the link.