Use an extension for Opera to set bookmark page in a new tab. There doesn't seem to be other ways to achieve that easily without using an extension.
Use either one of the listed extensions at above.
Latest version of Opera is preferred, although older versions may be able to install the extension.
Use Opera web browser to visit Opera add-ons website (link above). Check the extension name and its author name, to be sure.
In the right column of page, look for a green button + Add to Opera.
Click the button once, then wait for the button to change from "Installing" to "✓ Installed".
If installation was successful, the extension will be listed by "Extensions" tab in Opera.
Go to Menu > Extensions > Manage Extensions (or press Ctrl+Shift+E).
In "Search extensions" field, type a keyword like "tab" to filter name of extension, or scroll and search manually. Then, click Options for the extension.
Enter the URL of your choice. For bookmark page, type either:
opera://bookmarks (native) or
chrome://bookmarks (since Opera 15).
Click OK to finish.
The end result depends on how the extension work (read the description for each at link above). Ideally, user will just open a new tab as usual. Otherwise, user may have to click on a toolbar button, or such to achieve the result.
Bookmarks tab discrepancy
When "Bookmarks" tab is opened, "Unsorted bookmarks" is shown by default (Opera 42.0). Newer Opera will show "My bookmarks" (Opera 43.0) or "All bookmarks" (Opera 45.0). This behaviour seems to be non-customizable.
Tested using extensions for Opera, Custom New Tab Page 1.6.1 with Opera 42.0, 43.0, and 45.0; Homepage in New Tab 1.0.7 with Opera 45.0 and 57.0.