IMPORTANT!

BEFORE USING - MAKE A BACKUP (EXPORT YOUR LIST)

Instruction how to prepare and run the script:

1. Open Dev Tools (Right Mouse Button and Inspect Element or just F12) and click "Network"
2. Turn on the script, then go to https://anime.plus/ and write Your MAL profile name
3. After your data got loaded (refresh to see changes), go to history of anime, and the script will inform you about the start in the console
4. Let the script work, it will gather ids of titles that are missing dates, then redirect You to the 1st Anime from Your missing dates list - don't click anything, just look at the console, script will work in the background
5. After "The End" message, check in the "Network" tab if all the requests got status 200
6. Turn off the script
7. Check the dates
8. Enjoy

Script tested on Tampermonkey

MAL Post Link: https://myanimelist.net/forum/?topicid=1886650
Backup/Export: https://myanimelist.net/panel.php?go=export

btw. I guess it's obvious, but You have to be logged in on MAL

ps. The process might take a while, so please - be patient.
btw: Sorry for my bad english...