tablacus explorer added a menu to move the selected tab to the tab group in the tab menu (Requires usloader add-on)

move-tab-to-tabgroup.user.js

Sync.MoveTab = {
    Exec: async function (Ctrl, pt) {
        const tabs = [];
        const len = await GetLength(await te.Data.Tabgroups.Data);
        for (let i = 0; i < len; i++) {
            const name = await te.Data.Tabgroups.Data[i].Name;
            tabs.push({ index: i, name: name});
        }
        let hMenu = await api.CreatePopupMenu();
        for (let i = tabs.length; i--;) {
            let uFlags = MF_STRING;
            if ((await te.Data.Tabgroups.Click - 1) == i) {
                uFlags |= MF_CHECKED;
            }
            await api.InsertMenu(hMenu, 0, MF_BYPOSITION | uFlags, i + 1, (i+1) + ". " + tabs[i].name);
        }
        pt = await api.GetCursorPos();
        const x = pt.x;
        const y = pt.y;
        const nVerb = await api.TrackPopupMenuEx(hMenu, TPM_LEFTALIGN | TPM_LEFTBUTTON | TPM_RIGHTBUTTON | TPM_RETURNCMD, x, y, ui_.hwnd, null, null);
        api.DestroyMenu(hMenu);
        if (nVerb > 0) {
            const TCs = await te.Ctrls(CTRL_TC, false, window.chrome);
            for (let i = 0; i < await TCs.length; i++) {
                if (await TCs[i].Data.Group == nVerb) {
                    const TC = TCs[i];
                    const TC1 = await Ctrl;
		            const FV = GetFolderView(Ctrl, pt);
                    const index = await TC.Count;
                    await TC1.Move(FV.index, index, TC);
                    TC.SelectedIndex = index;
                    Addons.Tabgroups.Change(nVerb);
                    break;
                }
            }
        }
    }
}

AddEvent("Tabs", async function (Ctrl, hMenu, nPos) {
    api.InsertMenu(hMenu, -1, MF_BYPOSITION | MF_STRING, ++nPos, await GetAddonInfo("tabgroups").Name);
    ExtraMenuCommand[nPos] = Sync.MoveTab.Exec;
    return nPos;
});