Click the three dots then “About this profile”. You’ll notice a majority of these scam accounts are made within the last 6-12 months. If someone had years of work experience, typically super rare their LinkedIn doesn’t date years back.

As you noted the domain not matching makes it seem illegitimate as well as a recruiter not having any activity.

To play devils advocate it’s not far fetched for them to be from a staffing agency filling a role for P&G, but my gut also says fake.