[FEATURE REQUEST] Persist search between tabs

## Before submitting the issue

- [X] **I have checked that the requested feature is not a duplicate or, if it is, it needs to be reopened**
- [X] **I have checked that I am running the latest version of WingetUI**
- [X] **I have checked the [FAQ](https://github.com/marticliment/WingetUI#frequently-asked-questions) section**
- [X] **I have read the [contributing guidelines](https://github.com/marticliment/WingetUI/blob/main/CONTRIBUTING.md#feature-requests) and I agree with the [Code of Conduct](https://github.com/marticliment/WingetUI/blob/main/CODE_OF_CONDUCT.md)**

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

It frustrates me when I want to check if a tool is installed and if not, install it. I enter a term into the installed packages tab and if I do not find and switch to the discover packages tab I expect the search bar to stay the same, instead I have to reenter the search term.

## Describe the solution you'd like

I would prefer if the search bars always would contain the same text, or if there was an option for this.