Have you looked at hunchly - https://hunch.ly/ ? It indexes sites as you browse and let’s you search for content within them - and only the sites you hit, so its not crawling the rest of a domain. It’s built for investigations, really, but it sounds like it does what you’re describing. Its not free, unfortunately, and uses an installed program coupled with a browser extension to do what it does.
Have you looked at hunchly - https://hunch.ly/ ? It indexes sites as you browse and let’s you search for content within them - and only the sites you hit, so its not crawling the rest of a domain. It’s built for investigations, really, but it sounds like it does what you’re describing. Its not free, unfortunately, and uses an installed program coupled with a browser extension to do what it does.