If you set up the collection page of the Shopify theme "Dawn" to display a "Limited Time Left" label depending on the stock level, you can make it appear in the "Featured Collections" section with a little tweaking.
Example of setting up the "Dawn" theme's featured collection section to display a "Limited Stock" label when stock falls below a certain level

[(For the Dawn theme) Setting method ①] Add the schema to "featured-collection.liquid" and the label to "ja.schema.json"

[(For the Dawn theme) Setting method ②] Add code to "featured-collection.liquid" and "card-product.liquid"

