Unable to search TinyPic image URLs

**System**

* OS name: Windows
* OS version: 10
* Browser name: Firefox
* Browser version: 128.0.3
* Extension version: 6.1.1

**Bug description**

1. Go to: https://hardforum.com/threads/windas-white-point-balance-guide-for-sony-trinitron-crts.1830788/post-1041045250 and see this post has two attached TinyPic links.
2. Right click on the first image link - Unable to search wayback machine for image link (only entire forum page)
3. Right click on first tinypic image link, select open image in new tab
4. Right click on server error page to then search wayback machine for the tinypic image, image displays as expected in a new tab
5. Right click second image and repeat steps above - Incorrect archive image is retried (tinypic sorry image not available message instead of earlier archive of correct image)

Expected behavior: Right click on TInyPic URL allows searching in Wayback Machine without having to open in new tab first. Step 5 I'm not sure if there is a fix for that to make sure the default tinypic error message isn't the archive thats retrieved.

Thanks!

Start by reproducing the TinyPic cases from the issue in Firefox 128 with extension version 6.1.1, comparing the context-menu search with opening the image in a new tab first. Trace the Wayback Machine search flow used for image URLs and verify that direct searches work and do not select the generic TinyPic error image.

Written by the indexing model from the issue text.