Hi, I'm Bernard, a fellow Windows user. I'm happy to help!
For a 3-month game pass, it should show up in the account, and there is no need to redeem the code. Kindly check your subscription history if it's successfully activated: https://account.microsoft.com/billing/orders?ref=xboxsupport
If it doesn't push through, there might be an issue with the Microsoft Store. I recommend opening the Xbox app and redeeming it from there.
If the issue persists, I suggest resetting the Microsoft Store app and Xbox app by following the steps below:
Press the Windows key + R, then type in:
wsreset
Then hit OK
Method 2. Repair Windows Store and Built-in apps:
Press the Windows key + X, then select Windows PowerShell (Admin) or Terminal (Admin)
Copy, paste, and enter the command below:
Get-AppXPackage | Foreach {Add-AppxPackage -DisableDevelopmentMode -Register "_.InstallLocation)\AppXManifest.xml"}
Then hit Enter. Once the process is done, restart the PC and check.
For further assistance, you may check on this link: https://support.xbox.com/en-US/help/subscriptions-billing/redeem-codes-gifting/digital-code-solution
Answer from Lester Bernard Reyes on learn.microsoft.com