There's no such extension, but here's a workaround. Select a broken image frame you want to fix and open the XML Editor [shift+ctrl+x]. In the properties panel, you'll see that Inkscape links to external images like so.
You can use the Find and Replace dialog [shift+ctrl+f] to change path for multiple images simultaneously. [Find: file:///PATH_TO_LINKED_FILE] [Replace: file:///NEW_PATH_TO_LINKED_FILE] [Search in: Properties] [Replace All]
Perhaps you don't want to update all links in your drawing. [Options] [Scope: Current Layer] or [Scope: Selection]
By the way, this is a long-standing feature request. Here are two that I know of.
Beyond the Basics Relinking folder?
Inkscape.org
Based on what I know this _should be a lot easier than multiple steps for each linked image in each file..!
Is there not a way to tell Inkscape to look for broken images in a new folder (that I'd like to move/rename) and relink to those???
Or even a sub-program/extension that does this for all linked images in _all Inkscape files within a directory? Just a search/replace of a path?
At least, add search and replace to the XML editor?
There's no such extension, but here's a workaround. Select a broken image frame you want to fix and open the XML Editor [shift+ctrl+x]. In the properties panel, you'll see that Inkscape links to external images like so.
xlink:href file:///PATH_TO_LINKED_FILE/LINKED_FILE_NAME
You can use the Find and Replace dialog [shift+ctrl+f] to change path for multiple images simultaneously.
[Find: file:///PATH_TO_LINKED_FILE]
[Replace: file:///NEW_PATH_TO_LINKED_FILE]
[Search in: Properties]
[Replace All]
Perhaps you don't want to update all links in your drawing.
[Options]
[Scope: Current Layer] or [Scope: Selection]
By the way, this is a long-standing feature request. Here are two that I know of.
https://gitlab.com/inkscape/inbox/-/issues/2395
https://gitlab.com/inkscape/inbox/-/issues/5894