Hello, I analysed the problem further. I don't know why you have autofill_inline_suggestions_key set to true and I have it set to false, but I don't really know what all the properties correspond to, so that should be addressed on the developer's GitHub page.
I think I finally get the issue now. So, let's assume that the pop-up/toast for autofill always appears one way ore another, either automatically of by clicking on the field. What I understand by you wording is that it bothers you that no entry appears in the popup for that site even though you have correctly setup the URL in the entry, so the search option should find the entry.
Now, I was just trying to login on a website I do not visit often, and I got the same strange behaviour: pop-up appears but with no entry (I have to tap the pop-up, enter KeePassDX and search for it manually), even though I had the correct URL. Upon closer inspection I notices that the URL saved in KeePassDX had a trailing forward slash ("/"). I deleted it, and the autocomplete immediately found the entry automatically.
To test the hypothesis, I modified my entry for this forum, that always autofilled correctly, so instead of having "https://discuss.grapheneos.org" i put "https://discuss.grapheneos.org/" (the only difference being the "/" as a last character) and it does not work anymore!
So try this: in the entries that for you do not autofill, try delete everything after the TLD. So, e.g., if you have "website.com/login.php" delete "/login.php" and only keep "website.com" (notice that there should be no trailing forward slashes).
This seems consistent with a bug reported on their GitHub: https://github.com/Kunzisoft/KeePassDX/issues/1940
It seems like the search function badly matches the string and interprets "website.com/" as just "/".
This, however, is only a partial solution. Their search function seems to be very wonky. To further test the hypothesis, I created a fake "archive.org" login entry. Their true login page is "https://archive.org/account/login", to I tried leaving "/", "account", "account/", "account/login" and "account/login/" after the domain, and the autofill always found the entry. So this seems to (partially) invalidate the hypothesis.
But, with further speculation, all the websites where the "trailing forward slash" problem appear seem to have a subdomain for login, e.g. discuss.grapheneos.org. So maybe the search function does not correctly interpret subdomains.
For fun, I also tried accessing "accounts.google.com", since it's a website with a subdomain and Google always creates a very long URL with a unique token when trying to login. What I found is that on Firefox the autofill finds the entry, but on Vanadium it doesn't. So it seems also a Vanadium-related issue, but given what I found earlier I think the issue still lies in KeePassDX's search function. Maybe it's also connected to the HTML of the webpage one is trying to login on.
All this is, however, speculation that should be addressed on KeePassDX's GitHub issues page.