Can HomePod Mini announce calls?

I see what you mean. HomePod just can’t act as a “phone”. A better option for her might be some Bluetooth earphones. I have the BeatsFlex. I mostly use them for audiobooks but they can be used for the iPhone calls as well. What I like is they hang around my neck while I’m not using them and can’t fall off because the magnets lock them together. You just press the little buttons to control the phone and in her case it might be best if she left them in her ears to hear calls come in. They’re sold all over the place and will be cheaper elsewhere but this helps explain them: https://www.apple.com/ca/shop/product/MYME2LL/A/beats-flex-all-day-wireless-earphones-smoke-gray?afid=p238%7Csy1vwXQRU-dc_mtid_1870765e38482_pcrid_653067045501_pgrid_151113640761_pntwk_g_pchan_local_pexid__&cid=aos-ca-kwgo-pla-btb_lia--slid---product-MYME2LL/A-CA

Of course there are other Bluetooth options out there as well. There’s more expensive ideas like the Apple Watch. Calls come through that from my iPhone. I don’t like using my watch for calls but it at least lets me know I’m missing a call and I can go to my phone right then or when I’m free to do so.

It can’t announce calls.  Before answering, you can ask “Hey Siri, who’s calling?”

Use HomePod for phone calls - Apple Support