Would it be weird to email PI about application for Lab Manager position?

Hi all, I'm currently a lab tech with almost 5yrs of work experience, and I'm currently looking to switch the lab I'm working in at my uni. I applied for a lab manager position with a PI who is starting a new lab in a different dept, and I was wondering if it would be weird if I also emailed them about my interest in the position? Ik it is not uncommon for post-docs and such to cold email PIs, so that is why it is in my mind.

Also any advice on how I should compose such an email if so would be appreciated! ty in advance