How can I bypass HomeKit security restriction for hands-free garage entry using HomePod?

You really do NOT want to do that.

Imagine someone stealing your phone from your pocket while you're out. If you were able to do what you're asking for, they would have unrestricted access to your garage just by having the phone with them. No need to actually verify it's you.

If neither of the two unlock options works, and if Siri is set for unrestricted lock screen access (enter Allow in the search box), then send Apple your feedback:

• Unlock your door with a home key on iPhone or Apple Watch - Apple Support

• Feedback - Home App - Apple

You’re not going to find an official workaround for gaining entry into your home. It’s too much of a risk that an unwanted person could gain entry, whether it be to rob you or assault you. Even if you think it doesn’t apply to you, it may to others and it has to be universal.

MrHoffman wrote:

If neither of the two unlock options works, …

Ubiquiti equipment has the ability to read license plates and to scan faces, and can then be configured to use that to grant gate or door access. Keycards and fingerprints can also be used. Not that I’ve tested any of those access features anywhere, or the accuracy. That’s entirely within the UniFi Protect system too, and not involving HomeKit at all.