The default cursor gets lost in the document mode. Would like to darken, thicken or color it.
The behaviour of your mouse and cursor are controlled by your Operating System, not LibreOffice. You are using Windows, right? Try Control Panel → Mouse → Cursor → Magnified, or something similar. There are a number of options. (Windows 10 might be different too.)
Had the same problem with MS Word 2016 in Win10 (1903).
See this to optimize cursor size: Change Text Cursor Thickness in Windows 10 | Tutorials or https://www.ghacks.net/2019/10/15/microsoft-adds-a-text-cursor-indicator-to-windows-10 (option “make the cursor easier to see when typing”).
Unfortunately there seems to be no such option in Linux Mint 19.2 …