I wanted to shed some light on this issue since I too ran into this problem and was able to resolve it. Let me begin by explaining how I got to the point where only my home key (the owner of the house) worked and all the other users did not, and then the steps I took to resolving the issue. Maybe this will resolve your issue too, and give Apple some background on where to help troubleshoot a potential bug with the Home Key feature.
Background that led up to Home key not working for some users
I purchased a level lock+ back in December 2022. The installation, configuration was all straight forward and was working as expected, along with getting all family members setup with home key as well.
To clarify my order of sequence during setup: 1. I installed Level's app. 2. created an account. 3. setup a new lock in the Level app. 4. added users in the Level app. 5. I added the lock to the Home app. 6. I setup Home key on the Home app.
Ok, from here everything was working until Apple released the new architecture into Home. I didn't have issues with Apple Home, but my level lock had severe vampire battery drain - new battery would be gone in 2 days. I was also experiencing weird issues with Apple Home hub connecting to the lock (would get No response randomly) but after manually locking/unlocking the lock it would then synch and connect to my apple Home - I think this is besides the point. So I worked with Level's support to getting an RMA created for a new lock - this took WAYYYY too long (~3 mnth) But they finally got around to shipping me a new device. So once I got my NEW level lock, I deleted the existing one in the Home App and Level App, uninstalled the lock, installed my new lock and configured it as mentioned previously (setup new lock in Level's app, then added to Apple Home).
One thing different I did here though was I DID NOT invite my family members to use the NEW lock before I added the lock to Apple Home.
Anyways, when I grabbed my wife's phone to verify her phone's home key worked (I went to her Apple Wallet and saw a Home key in there so I assumed everything transposed automatically) and it wasn't working...After I did some digging, I realized, stupid me, I needed to add her to the NEW lock in Level's app. So I did that, and verified wife's phone could unlock/lock lock from Level's App, done. I tried her home key again and still "Try Again" error was coming up. I restarted her phone, and still same error.
The Solution
My thought process was maybe my wife's Home Key is not really the same Home Key linked to be used on the NEW Level Lock+ (maybe there was something that did not automatically update/change like I thought it would). There was no way to "delete/remove" her Home Key from the Apple Wallet app, so I decided to start with a clean slate. From my phone, I removed the NEW Level Lock+ from Apple Home and Level's App. After that, I made sure mine and my wife's Apple home Key disappeared from our Wallet. Then, I started the process over by setting up the lock in Level's App, inviting family members in Level App, and then adding the lock to Apple Home again. Once I did this, I was prompted to add a new Apple Home key to both my phone and my wife's phone. After that, Home Keys were working on both of our phones.
Sorry for the long write up. I hope this helps.