If you have added line items from your price books onto a favourite, then the standard pricing for them will update with changes to that price book item.
For example, if I add a line item from my custom price book into a favourite, then change that item's cost price when editing my custom price book the favourite will also update to use that new price.
In a similar vein, if I upload a new price file CSV from a supplier, then the standard pricing will also update for any of those line items in the favourites as well.
However, there is one situation to note: Line items that have an override or otherwise non-retail rule for their sell price in Tiered Pricing will still use that override or rule instead where that pricing tier is used.
Please note: Updating a product name does not update Favourites
There is a known issue where updating a product name in your price book does not update the product name stored against existing Favourites, even when the product code is unchanged. The pricing will update correctly, but the name displayed in the Favourite will remain as the original.
Until a fix is available, the only workaround is to manually update the affected Favourite names via Settings → Favourites.