I just installed the flatpak version of Libreoffice, and it uses the Breeze icon theme by default, and it doesn’t have the adwaita theme like the rpm version. I looked just about everywhere and couldn’t figure out how to install the adwaita theme.
Also on my RPM version of LibreOffice, there is no Adwaita theme. Elementary is used as the default.
The application icon set is provided by libre office, it can be modified by using extensions that are provided by volunteers at libre office.
You can find a list of available icons provided by libre office, here
You can then download them, they can be installed using the libre office extension manager.
Tools → Extension Manager