Add possibility to search run by test plan in 'Add to Run' modal (Tests tab)

[YanaBaranova0909]

Is your feature request related to a problem? Please describe.

In the 'Select unfinished run' modal (opened via 'Add to Run' from the Tests tab), each run displays:

• Run Title (included time stamp)
• Test Plan
• Test Count

However, search only works by the run title. This makes it difficult for users to find the correct run, especially when titles are similar.

CleanShot.2025-06-29.at.10.56.04.mp4

Describe the solution you'd like

Extend the search functionality in the modal to support searching by both:

• Run Title
• Test Plan Title

[littlefrontender]

@YanaBaranova0909 it needs backend improvements