You are correct: if the paragraph return also has been formatted with this character style, it wil be included in the found text. To make a GREP stop before an optional paragraph return, you can use
which loosely translates to "any consecutive run of characters of which none are a paragraph return".
Thank you Jongware. You rock!
Neither Find Text nor Character Styles have anything to do with lines. "Find Text" never selects an entire 'line'. Not even GREP can do this. (The Online Help for GREP contains the word "line" a couple of times [*] but it shouldn't, except in the negated sense of "GREP cannot distinguish a separate line".)
[*] From memory. I tried to verify this, but the Online Help failed to appear. Again.
... Adding Insult to Injury: a pop-up offering this:
Would you like to add Community Help search on Adobe® InDesign™ to your browser's list of search engines?
Well, I don't think so.
I'm kind of wondering why you would want to leave a character style applied to a paragraph break?