HomePod could not connect to the Wi-Fi network

Is this for a regular home network (SSID network name and password, but not ‘captive’)?

Verify that your iPhone or iPad is connected to the intended home network, then see the HomePod configuration in the Home app on mobile. If you see a mismatch alert, then click View Details, and Move HomePod to [same Wi-fi as mobile]. Set up HomePod or HomePod mini - Apple Support

For non-private networks using 802.1X and captive, see: Use your HomePod on an 802.1X Wi-Fi network - Apple Support.

With the mesh WiFi setup, be sure to turn Apple's "Private Wi-Fi Address" feature OFF on your iPhone BEFORE setting up your HomePod minis (if you've already gone through HomePod setup unsuccessfully, RESET your HomePods and redo setup after turning Private Wi-Fi Address OFF). The HomePod minis appear to try to make up a WiFi hardware address whenever they reconnect to the network. See Use private Wi-Fi addresses on iPhone, iPad, iPod touch, and Apple Watch - Apple Support.

Note that turning the 'feature' off will result in the words "Privacy Warning" being displayed next to your network's SSID in the iPhone's list of WiFi networks. You can safely ignore this. Frankly, the whole feature is the proverbial 'Solution in search of a problem'.