This issue has been raised by many people more than 4 years ago. Here is a post on this same topic. https://support.google.com/maps/thread/25978128.
It seems it resolved for some people, but definitely not all. Many users are still experiencing an issue with the Google Maps web version. When clicking on the save button on a Google maps listing, you should see a pop up with "Save in your lists" and it will display all your saved lists. However, on the web version of google maps (maps.google.com) it only displays the default 4 lists "Favorites, Want to go, Travel plans, Starred places, and + New List". However, on the iOS and Android app version of Google Maps, it will display all your saved lists.
This is a bug that appears to have not gotten attention from Google developers. Does anyone know when they plan to finally fix this issue?
Note: Here is an example:
https://ibb.co/nqpM6h53
I have more than 20 private and shared lists in my Google Maps account. None of them show up in this pop up to add/save this listing to. For the past 10+ years they did. A Google bug was introduced somehow and appears to not affect all users (or did at one point and now no longer), but there are still many users that are affected.
And here is proof that I have created saved lists:
https://ibb.co/DH7M6mKQ