Unless you want to leverage LinkedIn as part of your job search.
But even in that case, be mindful of the timing of the disclosure.
I have seen people do both. Some did not update their professional details till they found a new job. Others updated it as soon as possible to ensure they could find a new role.
It's a blue button called "open to". You can select "finding a new job". You may select this and other people checking your profile will see it.
In case of any troubling questions, you may claim you did not do it since it's nothing explicit like a post you wrote and shared
Also set the open for jobs option on your profile (visible to users with linkedin recruiter only).
Don't announce that you are in a notice period though.
Meanwhile, I have a very minimal profile and hadn't updated it in 8 years, and I recently got the best job of my career via a recruiter searching on LinkedIn. Life is funny ...
Try to talk to as many recruiters as possible, you will be in their database as actively searching and the words gets around / more potential opportunities are made.
Best of luck for your future!
I was once fired as part of a major downsizing exercise of a large company. Younger and more naive me accepted the request from my boss to keep it quiet as my team was launching a new product and he did not "want that noise" at the same time. I believed I should better do what he wants to not ruin my reference letter. Older me thinks I should have given him a swift kick in the balls to find out if that would also make a noise disturbing his product launch.
If you have a reasonable story why you are leaving - go out and tell the world you are looking for a job!