BitDefender Mobile runs on my phone and I don't do anything crazy with it
Somewhat off-topic, but IMO it's worth to remind that you need to trust them (since those antivirus ask lots of permission) and may drain your battery faster.
Am I being too paranoid here or should I just generate a new seed phrase when my new Cold Card Q arrives?
You're not being paranoid at all. IMO generating new seed phrase on your new ColdCard Q is similar with using different password or email on each internet account.