Is there any cleaning utensil that is comparable to fingernails?

Try searching for "pan scrapers." I have a pair from Lodge that has served me well, though you can find almost identical scrapers without the branding.

These are essentially equivalent to the scrapers mentioned by ChrisH, but with curves to make it easier to clean the edges of your pans

I feel your pain. Dough and sourdough starter seem to find ways of sneaking onto my worktop when I'm not looking, and drying there; as it's solid wood I can't soak them off, and do end up using my nails.

A few things things spring to mind, depending on the task:

• Plastic ice scrapers for freezers work on fairly large flat surfaces. (That's what I should use, but I can never be bothered to find mine)
• Some washing up brushes (often the cheap ones, not the one I have from Ikea) have a chisel-shaped scraper on the back. Here's a slightly unusual example.
• During cooking or on hot stuff, a flat wooden spatula is good (and very cheap). The one I've pictured tapers to a good edge for scraping. They can be reshaped with sandpaper if you like. I choose one for some cooking tasks so it's ready preemptively, to scrape before things burn on.

What about 100 fingernails all scraping close to each other? That is one way I would describe the Scotch-Brite Dobie "all purpose cleaning pad".

Here's a picture:

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It's a plastic mesh around a foam sponge, and it's safe on all non-stick and other surfaces. It's a bit gentler than the plastic scrapers in some other answers, which means it will take longer to get off stuck-on food. Also, the plastic mesh wears out and you have to replace them, whereas the scrapers can last forever.

One advantage of the Dobie over the scrapers or fingernail is that it has surface area to scrub a whole area, as opposed to just a blade-like profile.

Chopsticks. Take a few pairs of the cheap wooden chopsticks you get with takeout Chinese food and hold them together in a bundle

I keep an old credit/membership card next to the sink for this purpose.

I've used guitar picks for decades. They are in fact, artificial fingernails. Unfortunately, the music stores stopped giving them away free a few years ago. Now it's a couple, four bucks for a dozen Fender brand.

I find dough scrapers indispensible, also for quick dry cleaning of surfaces (where the straight edge comes in handy). Here is an image of one (they tend to be slightly more convenient when they haven't yet dropped on the heating elements of a dishwasher, but the important thing is the plastic edge).

A chainmail pan scrubber is what I use on my cast iron, pots, and pans that needs something extra to help get them clean. Essentially it is reusable steel wool, but not as abrasive.

I keep a plastic jar-lid lying around for this task. Peanut-butter lids are good, but the lids of the jars of actual peanuts are the same material, and ~2.5" in diameter (compared to ~3.5"), which I like better. We go through peanuts fast enough that there's never much concern about the scraper wearing out.

(These details may be different in your area, IDK. I'm sure lots of other consumables you use have similar pieces of hard plastic in their packaging. )

People have suggested dough scrapers; the one we have is distinctly softer than I'd want for this task. I keep a plastic jar-lid lying around for this task.

I've found plastic razor blades to be good for this. The ones I got came with a plastic holder that didn't work very well, but they're the same size as normal double-edged razor blades, so they fit a better scraper I got at the hardware store.

I have potscrubber pads made of loofah, a fibrous vegetable husk, which are not just effective, but also not made of plastic.

I got a pack of 5 from Amazon, because it's a bit exotic for our supermarket.

The Scrigit is specifically designed to mimic using one's fingernail for scraping.