Does this code in userChrome.css wor for you?

@namespace url("http://www.mozilla.org/keymaster/gatekeeper/there.is.only.xul"); /* only needed once */

.tabbrowser-tab:not([selected]):hover .tab-content { /* highlight on mouseover */
   background-color: #dbe3eb !important;
}

Yes, that does work, however it breaks my "Open a new tab" button, which no longer highlights on mouseover (only the '+' sign icon highlights, not the background of the button).

My code appears below yours. Without your code, the entire "Open a new tab" button highlights correctly.

.tabbrowser-tab:not([selected]):hover .tab-content { /* highlight non-selected tabs on mouseover */
   background-color: #dbe3eb !important;
}

#TabsToolbar .tabs-newtab-button {
  border-top: var(--classic_squared_tabs-border_size) solid var(--classic_squared_tabs-border2) !important;
  border-left: var(--classic_squared_tabs-border_size) solid var(--classic_squared_tabs-border2) !important;
  border-right: var(--classic_squared_tabs-border_size) solid var(--classic_squared_tabs-border2) !important;
  border-top-left-radius: var(--classic_squared_tabs-border-radius) !important;
  border-top-right-radius: var(--classic_squared_tabs-border-radius) !important;
  min-width: 0px !important;
  width: 28px !important;
  margin-bottom: 0px !important;
  border-color: #868b98 !important;
}

.tabs-newtab-button .toolbarbutton-icon {
 min-width: 0px !important;
 min-height: 0px !important;
 width: 14px !important;
 height: 14px !important;
 margin: 0px !important;
 margin-bottom: 0px !important;
 padding: 0px !important;
 box-shadow: unset !important;
}

I think that this has more to do with background: unset !important; When I remove this rule then at least I get some change on hover, but it is only a small box with your code.

Yes, I took the background: unset line out, and now only the '+' icon is highlighted on mouseover.

Is there a way to have the entire button highlighted?

By chance, I tried the following, and it works...

#TabsToolbar .tabs-newtab-button:hover {
    background-color: #dbe3eb !important;
}

.tabs-newtab-button:hover .toolbarbutton-icon {
   background-color: #dbe3eb !important;
}

Didn't need the not([selected]) attribute, so I removed that as well.

Thank you :)