Can I turn on WiFi on my Mac but keep using my wired Ethernet connection for internet access?

Yes you should be Able

Aspects from the Support Doc from Apple is below

How to set up Auto Unlock

Make sure that your devices meet the system requirements for Auto Unlock and are set up as follows:

• Your Mac and Apple Watch have Wi-Fi and Bluetooth turned on.
• Your Mac and Apple Watch are signed in with the same Apple ID using two-factor authentication.
• Your Apple Watch is using a passcode.

If your Mac is using macOS Ventura or later:

1. Choose Apple menu  > System Settings.
2. In the sidebar, click Touch ID & Password (or Login Password, depending on your Mac model).
3. In the Apple Watch section on the right, turn on the setting for your Apple Watch.

If your Mac is using an earlier version of macOS:

1. Choose Apple menu  > System Preferences.
2. Click Security & Privacy.
3. Select ”Use your Apple Watch to unlock apps and your Mac” or “Allow your Apple Watch to unlock your Mac.”

Full link below to cross reference

Can I turn on WiFi on my Mac but keep usi… - Apple Community