Hello jaroslav243,
Thank you for reaching out in Apple Support Communities. You've done an excellent job with the troubleshooting steps that were performed. One other step is to ensure that the HomePod mini is updated to the latest software. This helps provide software improvements that may help you in this situation with voice recognition. If needed, here's how to update the software on your HomePod mini:
1. Make sure that your device is updated to the latest version of iOS, iPadOS, or macOS.
2. Open the Home app.
3. Tap or click the More button , then Home Settings > Software Update.
4. If there's a new update, select Update. If there isn't a new update, you can select HomePod to turn on automatic updates and get the latest software automatically when it's available. Software Update also tells you if your HomePod is already up to date, and shows you the installed HomePod software.
A white spinning light appears on the top of HomePod while it's updating. The update might take some time. Make sure that your HomePod stays plugged in while it's updating.
These steps are outlined in this helpful article: Update HomePod - Apple Support
If that doesn't help, we recommend to contact Apple Support. They can review this further. Here's the link to contact them: Apple Support
Best regards.