How to add fancy borders to the entire page in LibreOffice Writer

What do you want to achieve exactly? If you just want to modify the appearance of LibreOffice, without modifying the output, you could set a custom color for the document background: Menu "Tools" -> "Options" -> "Appearance" -> "Document Background".

If you want to modify the output, too, you will need to use a workaround, since you can only modify the area inside the page margins (as laurent described). just modify the page style (as described below under "Edit").

To modify the page appearance in a printable way, there's a nice workaround: Don't touch the page margins, but insert the content (full-page watermark, stationery, or just a full-page frame with a certain background) into the header / footer. This way, it will modify each new page, too. To modify the "background color" of the complete page, you could proceed as follows:

That's it - now you have a frame as "background object" on every page, thus effectively setting the page background.

See also the accepted answer in this ask.libreoffice.org thread.

EDIT

In current versions of LibreOffice (tested with 6.4), it's possible to set the page background color in the Page Style Options:

1. Open Menu Format;
2. Select Menu Entry Page Style...;
3. Select the Area tab;
4. Default for Area is None; select Color instead;
5. Select the desired Color;
6. Click Apply.

That's it, the Default Page Style now has a colored background. To test it, simply export an empty writer document with background color as PDF; the PDF will show the selected background color.