Is your feature request related to a problem? Please describe.
On Profiling, we'd like to filter the flamegraph when navigating from one page to another. That means I need to save in the URL the search value the user provides and pass it down to the flamegraph component. In case the user edits or clears out the search value I need to update its value in the URL too.

Describe the solution you'd like
The solution I propose is to expose two new properties: searchText and onSearchTextChange.

The first one searchText, is an optional string that will be used to pass down the searched value.
The second one onSearchTextChange, is an optional callback function with the new searched value, in case the user edited, or undefined, in case the user cleared the search.

<Flame
    id={id}
    columnarData={columnarData.viewModel}
    valueAccessor={(d: Datum) => d.value as number}
    valueFormatter={(value) => `${value}`}
    animation={{ duration: 100 }}
    searchText={searchText}
    onSearchTextChange={(newSearchText: string | undefined) => {
      //update url based on the new text
    }}
  />

Describe alternatives you've considered
N/A

Additional context
N/A

Kibana Cross Issues
https://github.com/elastic/prodfiler/issues/3126