I just noticed that LibreOffice was not correcting my spelling as I was typing. That seems like something that should be included by default. My solution was to install hunspell.
sudo apt install hunspell
Then in LibreOffice go into tools > language settings > writing aids and in the "Available Language Modules" block put a check-mark next to "Hunspell Spellchecker".
After that it LibreOffice should be able to check your spelling as you type.