I'm seeing similar, except I can tie it down specifically to the 'mini'. I have three original HomePods (one standalone, one stereo pair) and 5 HomePod Minis (three standalone and one stereo pair). All are on iOS 15.4.
If I ask an original HomePod to set a timer, no problem. It does it straight away.
If I ask any of my minis to set a timer I get '<pause>One sec... <pause> Still on it... <pause> Sorry, that was taking too long'.
No number of soft or hard resets is fixing it and I'm not having any issues with my watch, phone or iPad.
All of the other Siri requests I've made seem to be working (though I had to reboot one as when I asked it for the outside temperature it said it didn't know where I was).
This feels like a software issue specific to the minis to me, I've stopped just short of doing a full factory reset and re-install of one as we really shouldn't have to be doing this every time there's an update (I've already done it several times since buying these things).