[Firefox] Open tabs in the same container as the original tab

[WPMGPRoSToTeMa]

Is your feature request related to a problem? Please describe.
I'm using the Tab search mode and when I click on Wayback Machine/Google/etc. a new tab opens in No Container no matter what container the current tab was in.

Describe the solution you'd like
An option to open new tabs in the same container as the current tab (when the Tab search mode is active).

Describe alternatives you've considered
N/A, but probably Temporary Containers is able to automatically re-open these tabs in a new temporary container(s). Not the same as proposed, but still better than No Container.

Additional context
https://developer.mozilla.org/en-US/docs/Mozilla/Add-ons/WebExtensions/Work_with_contextual_identities