nit: A bit cleaner approach is to move this logic into a separate function named like getBackfillStatusColor() implemented via switch like

function getBackfillStatusColor(status: BackfillStatus): IconColor {
  switch (status) {
    case 'pending':  return 'warning';
    case 'running': return 'success';
    default: return 'subdued';
  }
}

Auto refresh interval is set to a magic number 3000. It's worth to add a constant.

I'm curious though why 3000 has been chosen.

nit: It looks like a good idea to have one or more shared constants for refresh intervals and reuse them. For example rules management table has auto refresh functionality with a longer interval.

It's kind of random chosen, I try make balance between to fast, as group can be disappear, but also not make it to long that user wait long time

nit: 10 items per page is also a magic constant.

It looks like columns configuration could be moved outside component's body. For example defined below the component as const BACKFILLS_TABLE_COLUMNS = .... Though taking into account it can be extended with stopAction it's even better to create a separate function named like getBackfillsTableColumns(hasUserCRUDPermissions: boolean): Array<EuiBasicTableColumn<BackfillRow>>.

nit: Should it reuse already existing page sizes used for the other tables? If not it's still worth to have a constant for page sizes used here.

I'm curious if all that data is required for the test. It looks like it could be shrieked to bare minimum like id and using of @ts-expect-error with a comment will help to solve typing issues.

By some reason I like to have full data structure here, as it can help to easily see what can be in response

This type has too many fields for an inlined type. There is a type BackfillRow which has the same fields plus some extra. I should be much better to have a separate type containing inly these fields and defined BackfillRow as a union of this new type and Backfill.

nit: I encounter reduce quite often in Kibana's codebase. IMHO it has worse readability than for of. WDYT?

It can be more readable sometimes, but for this use case It think it's fine

Just to be precise this task returns table rows instead of the table itself. Either this function should be renamed to getBackfillsTableRows or it should return the table DOM element.

This line isn't necessary with toMatchObject.

Ideally this function should be placed below RuleBackfillsInfo. It will improve readability since a reader first sees exported component and then implementation details.