Are fillers suitable for hollows under the eyes?

I am looking into the phenomenon of sunken under-eyes as one ages.

I heard that if the areas under your eyes are sunken, you can look more tired than your actual age or have a gloomy impression.

It is said that getting under-eye fillers can improve the situation to some extent, but since the skin around the eyes is thin and sensitive, it is not easy to make that decision readily.

I heard that if the filler is injected incorrectly, it can become bumpy or unnatural.

I am wondering if fillers are a suitable procedure for the hollowness caused by the loss of fat under the eyes due to aging.

I would like to know if it simply involves filling in sunken areas, or if other procedures are necessary depending on the condition of the skin under the eyes.

I am also curious about how long the swelling or bruising lasts after the under-eye filler procedure.

Since it is near the eyes, I am worried that it might cause inconvenience in my daily life during the recovery period.

I would also like to know how long the effects usually last after a single treatment.

Please advise on whether older men can achieve a natural improvement and what to check first when considering under-eye fillers.