HomePod 15 beta 3
The upcoming HomePod 15 update includes a lot of features, including SharePlay and support for lossless audio. The third beta of the HomePod 15 software now adds lossless audio for the HomePod and HomePod mini. When Apple introduced it on other devices, the company promised that support for the HomePod would come. It was in the first beta, it was taken out in the second, and now it's back in beta 3.
Do you have iOS 15 on your device and the latest beta of the HomePod 15 software? (which you can install by invitation only), then you can go to your profile in the Home app and then go to Media > Choose Apple Music for lossless audio. If you play a song that is available in lossless quality, this will be shown as an icon in the music player. If you don't have a beta yet, you can already play lossless music on your HomePod via AirPlay, but this works in a roundabout way.
Fixed problems, but not all
Also good news is that beta 3 solves an annoying problem. Many HomePod owners have complained of sudden shutdowns and overheating that prevented them from using their speaker. The HomePod 15 release notes do not state which issues have been resolved.
The issues also exist with version 14.6 of the HomePod software, but no fix has been released yet.