I have the exact same issue and hopefully the info below will help for clarification of a potential hardware issue your HomePod.
With the popping sound and then the HomePod disconnecting and resetting itself after 2-3 minutes it is best to check on the iPhone, the HomePod been set up with, for a possible hardware issue.
Using your iPhone you can do this by:
1.Going into the Home App, selecting the HomePod that makes the popping sound by pressing your finger onto its icon and it will open the settings for this HomePod.
2.Scroll to the bottom and on the right there will be a grey cog icon (the HomePod's settings) and tap on this.
3.Another menu will pop up with all the various settings for the HomePod but you need to scroll down to Analytics and Improvements and tap on this menu.
4.There will be another menu that reads Analytics Data and you need to tap on this. This menu will then show lines of text of what the HomePod does when running in the background. You need to look at a line that starts panic-full (you should see the date(s) of when the popping occurs and there will be a time recorded which will match up to when the popping sound and disconnect happens.
My HomePod has just done 2 separate popping noises and then reconnected to my iPhone. In my Analytics Data is shows the following:
panic-full-2021-11-18-121115
panic-full-2021-11-18-121434
Those figures that read 121115 or 121434 means time recorded of 12:11pm (and 15 seconds) or 12:14pm (and 34 seconds) which is approximately 3 minutes between each popping noise, disconnect and then reconnection.
No amount of resetting/unpairing with the HomeApp will change this. Sadly, it is a hardware issue and the only way forward is to replace the HomePod if it's still in warranty/covered under consumer law that applies to the country it's been bought from or pay for an out of warranty replacement as long as the HomePod is in stock. If it doubt always seek advice at an Apple Store or call/chat with Apple Support. They are there to help...