NetBeans 11.1 was released almost two months before JDK 13, and while JDK 13 may appear to work fine with NetBeans 11.1 there are limitations, and it is definitely not officially supported. From the Product Manager for NetBeans: "Apache NetBeans 11.1 supports JDK 8 to JDK 12".
So if you want to use JDK 13 with NetBeans, download and install Apache NetBeans 11.2. The resolution looks fine to me when starting NetBeans 11.2 with JDK 13:

Regarding your "enlarged" concern, note that you can:
- Change font size in the edit windows by holding down the ALT key while scrolling with the mouse.
- Change the font size used by NetBeans in menus, dialogs and views by specifying the
--fontsize
parameter:
- You can do this temporarily by providing
--fontsize
as a parameter to netbeans.exe at startup.
- You can do it permanently by editing the configuration file netbeans.conf.
See FaqFontSize for more details.
Open a new question if you still see the same issues when using JDK 13 with NetBeans 11.2.