I no longer have my HomeKit setup code

Ignore it if it’s asking because there is no homekit code. Or tap Don't Have a Code.

If you do the set up as instructed in the link I provided, once done you will see it in the home app.

Review the entire page on Set up and use HomePod - Apple Support to see what else it can do.

The HomePod might need a software update, set it to automatic. It should be on 12.3

• About iOS Software Updates for HomePod

https://support.apple.com/en-ca/HT208714

• Learn how to update the software on your HomePod.

Make sure you did this part:

Get started

• Make sure that your iPhone, iPad, or iPod touch is updated to the latest version of iOS.
• On the iOS device that you use to set up HomePod, make sure that you signed in to iCloud with your Apple ID and turned on iCloud Keychain. You also need to have two-factor authentication set up for your Apple ID.
• Make sure that your iOS device has Bluetooth turned on and is connected to your home Wi-Fi network.*
• Make sure that the Home app and Apple Music app are installed on your iOS device. If you deleted either of these apps, go to the App Store and redownload them.

Read the article. You don't set up HomePod using the Home app. See Set up and use HomePod - Apple Support, make sure you meet the prerequisites set out in the Get started section, then follow the advice in the Press the top of HomePod to reset it section of Reset HomePod - Apple Support to set things up from scratch.

tt2

HomePod has no set up code, it will self install in the home app

Set up and use HomePod

https://support.apple.com/en-ca/HT208241