There should be an option to add things from your Plex library to the Watchlist from the show/movie selection instead of having to search each one manually and add it from the main search results.[mod-edit: this feature is available if the library is using the current-generation Plex agents]
There should also be a remaining episodes count on the watchlist tab for tv shows similar to the way it shows in the actual tv show list from your server.
The only browser extension I have on Chrome is 1Password and I had already cleared all browser cookies & cache prior to replying. I tried in both Chrome & Safari on my laptop and for an extra isolation proof this is what it looks like on my iOS App.
Disabled 1Password on Chrome and reloaded, no change. No change on Safari either. Correct, no options under ellipsis and no preferences I can see anywhere in any of the settings that would enable/disable the option.
Are these media actually located on your own server or are they on a shared server?
Add to Watchlist can only work, if the server owner has converted the libraries to use the new, native metadata agents. If they are still on the old agents, this won’t work.