Keep it a secret because there is no benefit. A coworker can mention your planned departure offhand to someone else who then mentions it to your manager and then bam, your life is made absolute hell.
Anytime some bullshit happens at your work that reminds you that you need to leave, take that fucking spite and put it into job applications. Do the applications on your employers time only. Get the bare minimum expected from you done and then spend the rest of the time applying.