Add search support

[victorpopkov]

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

I'm always frustrated when searching for some options. It would be nice to search through all possible options right in the menu, so that I could find things easier.

Describe the solution you'd like

1. Add a non-interactive search input in the menu just to show the current input value.
2. Bind keys to the menu and display the current input value in our search input.
3. Filter options based on the input and display only the matching ones.

Describe alternatives you've considered

If applicable, add a clear and concise description of any alternative solutions or features you've considered.

Additional context

If applicable, add any other context or screenshots about the feature request here.