I came here looking for a solution to my 1Password woes as well. I love Kagi, and through it loved when I found Orion (paying for both). But unfortunately the 1Password extension definitely isn't great.
Now, 1Password has always been flaky (if I had infinite time, I would have migrated to an alternative, but it's what I use, and what I taught my family to use, so we're stuck with it for now).
As for reproducing the issue, the 1Password integration fails to work (no icon in the text field, and the "autofill" button in the extension pop-up also doesn't work) on most websites I've visited so far, but not all.
I just tried news.ycombinator.com, and it does indeed work 100% of the time there. In contrast, this website, and on youtube.com (which redirects to accounts.google.com), the extension did not load, and autofill does not work, reloading the page multiple times does not help.
The fact that the devs are active here and asking for reproducible steps makes me optimistic that this will be fixed soon. For now, I'm accepting the inconvenience due to all the other amazing features I get in return (to me, it's Safari, but with an actual good sidebar tab view), but it's definitely a paper cut I could do without in my daily work.