Activate Siri and then say the amount of time you'd like on the timer. For me, that's holding the side button then only saying, "20 minutes."
The one caveat is that once the timer you want is two and a half hours or longer, then Siri replies by asking what you would like to convert to.
My Siri-initiated timers are always done with my phone, probably 50 or more each week (work stuff). The only time I get a failure is when I release the side button too quickly. I've made certain the spoken feedback is enabled to reduce the risk of me making that mistake. (Settings > Siri > Siri Responses > Prefer Spoken Responses)
As for, "What time is it?"... Try activating Siri and only saying, "Time."
That may be it - we’re always asking a HomePod to do it - “hey siri set timer for five minutes”