When using the search facility within the App [either web browser or smartphone] for a keyword, or phrase, the results may appear under two different headings depending upon where the search term is found :-
TO-DOS - where the keyword was found in the title of the entry.
NOTES - where the keyword appears in the body of an attached Note.
Depending on the length of your user-id {used for accessing your Microsoft "To Do" List Manager} you may experience an undocumented issue where the icon of a 'magnifying glass' that is normally displayed next to your user-id near the top left corner on the PC or laptop screen is nowhere to be seen.
Searching the web in general and specifically Microsoft's own Help pages yield nothing.
I decided to investigate and logged on to the To Do App using a few different length user-id's that i have access to. Typically the users id's are around 18 to 21 characters in length {something like xxxx.yyyyyy@gmail.com} and these worked fine. However when I used one that was longer than was actually 25 characters long {like xxxxxx.xxxxxxxx@gmail.com} the problem arose.
Then I had a sudden 'light bulb' moment and realised the longer sign-on id was actually filling the user-id box, of the To Do App on screen, and was displacing the wee 'magnifying glass' icon.
After fiddling around a bit I noticed that when you select the box with your user-id in it then move the mouse cursor to the right end a wee pop-up message appears on screen saying "Search" - if you then click here it will open up the full Search Box [temporarily replacing your user-id] and you can happily search for anything you like.