Search your annotations on hypothes.is from the browser search bar itself.
I'll describe the steps to do this on Chrome; it should be similar in any other desktop web browser :
Use the hypothes.is browser extension - no brainer, i know. Use a hotkey for activating the extension easily.
Set via.hypothes.is/google.com as the homepage in your mobile browser. Now, hypothesis will be activated on the google search homepage, on the page that loads your search results after you search for something using the search bar on the homepage, and every subsequent webpage you visit after clicking links from these pages. Yey!
The hypothesis search bar only searches the text in the annotation and the text in the url not the title. But you often remember a webpage by its title and sometimes the url does not contain the title text. So, it is good practice in my opinion to highlight the title of a webpage, so that it shows up in the search results.
If hypothesis keeps logging you out of your account it is probably because third party cookies are disabled in your web browser.