Good day to you. I've had this exact issue setting up multiple users on a single PC. Your instinct is right, it should work fine, but Phone Link gets sticky with account data.
The problem is almost always that the app on the second account is still trying to use the first account's credentials (even if you sign out). The fix is to basically factory reset the app on the second user's profile.
Here is the quick fix for the second account:
- Check the PC Account Type
Phone Link only works if the Windows account is linked to a Microsoft Account.
Log into User 2's Windows account.
Go to Settings → Accounts → Your info.
If it says "Local Account," click "Sign in with a Microsoft account instead" and use User 2's personal email to sign in.
- Reset the Phone Link App
This clears out all of the corrupted sign-in data.
Still in User 2's Windows account, go to Settings → Apps → Installed apps.
Find Phone Link, click the three dots (∙∙∙) → Advanced options.
Click Reset.
- Pair the Phone Again
Start the setup fresh.
On the second Galaxy phone, open the Link to Windows app and Sign out completely.
On the PC, open the Phone Link app. It will ask to be set up.
Follow the steps, scan the QR code, and when the phone asks, ensure you sign in with User 2's Microsoft Account.
That should completely separate the two connections and get the second phone working! Let us know how it goes.