Your browser instance stays the same as long as you operate within the same browser tab, even if you navigate somewhere to a different URL. The browser instance does not store the URL in any way. It just stores an Id that allows PAD to target the specific tab, and that's it. Even if you navigated away manually to some other page while your flow was paused, it would still work under the same browser instance. So, you don't really need to do anything and simply provide the same browser instance in there.
That is, of course, unless the new page opens in a new tab/window. In that case you need to use the Launch new {browser} action but make it attach to an existing instance, instead of launching a new one.
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