[edit] this post is now irrelevant, at first I didn't notice how to edit my question.

Enter about:config in the address bar and set browser.urlbar.autoFill.adaptiveHistory.enabled = true, then restart the browser.

Bookmark the page, then edit the bookmark and give it a Keyword so that it autofills.

browser.urlbar.autoFill.adaptiveHistory.enabled=True did not help , I was too quick to press the "Helpful / Solved the problem". I guess I need a 2nd coffee today.

Bookmarking momentarily fixed the issue.

[edit] edited to reflect latest findings

Again I was wrong :(

Bookmarking the site at first worked ... but failed later and the 1st suggestion went back to the "base URL".

I tried with the bookmark and a combination of browser.urlbar.autoFill.adaptiveHistory.enabled=True & False, still no luck.

You can not do this via about:config but can only do this via a bookmark, either a normal bookmark like created on the Bookmarks Toolbar that you click or a keyword bookmark where you type the keyword in the address bar and press Enter to open the URL connected to the keyword in this tab.

Type the Keyword you gave the bookmark exactly in the address bar and it will autofill. Make sure you filled the Keyword field of the bookmark and not the Tag field.

Bookmarking + a Keyword works but it's not the best.

For example, if the Keyword is "kkuukk-device", the suggestion doesn't show up until there's an exact match and this requires all letters "kkuukk-device" to be typed in. That's a bit of a surprise.

But I just tried something else. I have in my Browsing history facebook.com and www.facebook.com. If I type facebook.com or www.faceb , the 1st suggestion isn't facebook.com or www.facebook.com , Firefox shows "Search" suggestion, and following those Search suggest are Firefox suggest and that has facebook. So it look like there's some logic that works differently, perhaps depending on DNS results - can't really tell with a few tests that I did.

I still think Firefox should offer an option to suggest or not the base URL. Without such an option, the faster way for the end user to pick the proper URL requires switching from keyboard to mouse, and back to keyboard. That's not efficient at all.

Perhaps developers at Mozilla aren't hardcore like me/others that runs 20+ containers for many services (DNS, home automation, VPN, etc)? I'd rather have in my suggestion the latest page that I visited from a website (ebay.com/item_number/.... instead of the root domain "ebay.com". More then often, I tend to visit the last page that I visited from a site, not the base/root URL.

You can put Firefox Suggest higher by disabling "Show search suggestions ahead of browsing history in address bar results".

adaptiveHistory mentioned previously should autofill full URLs that are regularly visited.

Disabling "Show search suggestions ahead of browsing history in address bar results" didn't help.

If "Browsing history" is enable, Firefox suggests the base URL " https://device.domain.com/ " even if that's not in the Browsing History, only https://device.domain.com/admin is in the history.

I did another test. Deleted all history related to this device. Then Firefox doesn't suggest the base URL but right after visiting " https://device.domain.com/admin " , Firefox starts to suggest the base URL. This test was also done with "Show search suggestions ahead of browsing history in address bar results" disable.

I'm also looking for a solution to this. In fact, I opened another question before I found this one. My question at https://support.mozilla.org/en-US/questions/1439098.

I wrote this over on my question: "I went through all the browser.urlbar.suggest.* options, and even the docs at https://firefox-source-docs.mozilla.org/browser/urlbar/preferences.html. It would be nice if there was setting something like browser.urlbar.suggest.domainOnly, but looks like no such setting. Maybe someday the Devs can add this."

Update: I just discovered that hitting the tab key skips over the domain-only to the first suggestion after that. Which for me gets to 99% of what I was hoping for.