if (Translator.BetterTeX && !Translator.options.exportFileData && zotero.attachments && zotero.attachments.length) {
  for (const att of zotero.attachments) {
    if (att.localPath) {
      att.localPath = att.localPath.replace(RegExp("^\/.*?\/.*?\/"), "~/")
    }
  }
  tex.add({ name: 'file', value: zotero.attachments, enc: 'attachments' })
  return { cache: false }
}

It is possible to export Zotero items keys while using BetterBibTeX with this little postscript:

if (Translator.BetterBibLaTeX || Translator.BetterBibTeX || Translator.BetterTeX) {
    reference.add({ name: 'key', value: item.itemKey});
}

So the .bib will contain key = ITEMKEY so we can reconstruct a Zotero URI: zotero://select/library/items/ITEMKEY

You might find this workaround useful:

1. Close Zotero.
2. Open your Zotero profile folder.
3. Inside this folder, create a sub-folder named chrome.
4. Inside the folder chrome, create a file named userChrome.css with the content below.
5. Save. Reopen Zotero and enjoy.

Tested on Linux Mint 21.2 with the default dark theme.

.tabs::before,
.tabs::after {
    border-color: var(--tabs-border-color, rgba(0,0,0,.3)) !important;
}

.tab {
    background: inherit !important;
    color: inherit !important;
}
#tab-bar-container .tab:not(:last-child) {
    border-color: var(--tabs-border-color, rgba(0,0,0,.3)) !important;
}

#tab-bar-container .tab.selected {
    background: inherit !important;
    border-color: var(--tabs-border-color, rgba(0,0,0,.3)) !important;
    border-top-color: var(--tabline-color, #0a84ff) !important;
}

#tab-bar-container .tab:not(.selected) {
    border-bottom-color: var(--tabs-border-color, rgba(0,0,0,.3)) !important;
}

#tab-bar-container .tab:not(:first-child) .tab-close {
  filter: invert(0.7);
}

#zotero-toolbar {
    background: inherit !important;
    border-bottom: inherit !important;
}

Since I had to dig the code to understand how the plugin works, here is a little how-to:

1. Install MunGell/ZotServer on Zotero. It will launch a local server with a search endpoint at http://localhost:23119/zotserver/search
2. Open a note and type z@. A little search bar will appear to let you select the document needed.
3. Done.