General question about 2FA

If everything is working properly, it does not in any way interfere with a device's daily use? There have been posts by people stating they randomly get requests for a signing that requires a verification code.

As far as I know it is. Older ones (2nd and 3rd generation) require a different procedure that is described in the "What if I use two-factor authentication on a device running older software?" section of Two-factor authentication for Apple ID - Apple Support

I can't help with the Homepod part of the question but I have had two-factor turned on in my iPhone and Mac since it was first available and I don't find it to be any trouble. I have never had to enter a code again on either device except in Firefox or Safari; what I have found with internet browsers is that every time I log in to https://appleid.apple.com/#!&page=signin

I need a code; I suspect that may be in order to increase the security on that specific site as it is where you go to change passwords and other sensitive information. Most people would rarely go there but I do it relatively frequently to verify information when answering questions on this site. I have also found that maybe every 2 weeks to a month I need a code in order to log into icloud.com or this support site from an internet browser.