Hearing aids don’t require a prescription from a doctor. However, many are configured to a user’s particular hearing loss by an audiologist, so getting one may involve multiple visits to an audiologist. The audiologist tests your hearing loss at different frequencies, then configures the hearing aid’s equalizers to boost sound at the particular frequencies you have hearing loss, such that ideally your hearing at each frequency across the full frequency spectrum matches desired, when using the hearing aids. The audiologist can also apply a mold to your ears, such that the hearing aid is manufactured to your particular ear shape, making wearing the hearing aid more comfortable.
If you have notable hearing loss, this configuration by an audiologist can be invaluable. OTC products are getting more advanced. Some even support multiple equalizers that are configured based on hearing testing at different frequencies, similar to an audiologist. However, it sounds like the one you are describing, with a selection of 4 volume levels, is more basic. A simple up/down volume control is inadequate for many persons with hearing loss. It’s fine to try a cheap OTC product out and see if it works for you, but a person with notable hearing loss is likely to have a far better experience with a hearing aid configured to the user’s hearing loss and manufactured to the user’s ear shape.
Regarding the OP’s question, this is one of the many reasons why I prefer watching movies at home. I always have closed captions on. The Downton Abbey movie the OP mentions is supposed to be available on Peacock, starting on Wednesday of this week.