Symbols in my watchlist do not contain the drawings I made on charts

Layouts and charts are in no way connected to watchlists. Generally, watchlists can be treated as separate widgets that are account-wide, not belonging to a particular chart or layout. This means that you can switch to a different layout - which is basically a different workspace for your charts and trading analysis (more on that below) - but the watchlists will stay intact, you'll see the same watchlists on the right-side tool bar.

Now about layouts. As it was mentioned already, layouts are basically separate workspaces that can be somewhat compared to paper sheets or documents in a folder. They do display the last symbol you were charting when you look at the layout list, but they are in no way related to those symbols. So it doesn't matter if you named your layout after a symbol resolved on your chart and therefore think you associated it with that symbol now. No, layouts and charts/symbols are not linked in that way.

Thusly, those different symbols/charts are not different "documents"; they are interiors that belong to one and the same document, one layout. Imagine having one Google document and opening it in two browser tabs or two different computers. Same can be applied to our layouts. So you don't really need to save 10 different layouts unless you need to have 10 different charts of the very same symbol for instance.

So, the list of your saved layouts can be found here:

If you wish to learn more about layouts and how multiple charts are saved per one symbol, please refer to this article.