There are some settings in your profile that show you are open to work without broadcasting it on your profile picture. There is also a setting that is supposed to hide the fact you said you were open to work from people at your company but I’m not sure if that really works.
Have used this feature, works exactly like this. However it is a hit or miss, most of the incoming recruiters/companies are far below my standards. The best way to use LinkedIn is to send out requests to engineers where I want to work and ask for referrals. It's important to do your homework on the role, company, and person. Most of the people are happy to refer if you do this.