I agree with Slim. It's quite clear that the English Language translation of accidental implies that it is not on purpose. Therefore it's adaptation for referring to music notation is quite logically used to define an aberration or deviation from what is prescribed in the key signature.
To call the sharp symbols or flat symbols in the key signature itself "accidentals" seems very counterintuitive and the usage thereof in that context likely evolved from the simple fact that when we see a sharp or flat or natural sign on a music staff other than in the key signature - those symbols are commonly referred to as "accidentals". That does not mean that when the same type symbol occurs in a key signature - that it should also be called an accidental.
The word accidental technically refers to the fact that the note pitch deviates from the key signature - not they symbol itself. So technically, the symbol is either a "sharp symbol", a "flat symbol" or a "natural symbol" not an "accidental". The accidental is the occurrence of a note value that is not consistent with what is indicated in the key signature - not the symbol itself that is used to indicate the deviation from the key signature.
But it's easier to say "accidental" to refer to the symbol that is used to notate an accidental - rather than say sharp symbol, flat symbol or natural symbol.
So a more appropriate English word to define the sharps and flats in the key signature that are not accidental but on purpose - should we desire a single word (like accidental) - might be "incidental". The sharps/flats in the key signature are incidental to the key - not accidental.
Google list the following as synonyms for the word "incidental"
synonyms: connected with, related to, associated with, accompanying, attending, attendant on, concomitant to/with
"the risks incidental to the job"
If a set of sharps is incidental to a key that means they are connected to the key or accompanying the key or concomitant to the key. None of the other words with similar meanings sounds as appropriate to use in contrast to "accidental" as "incidental".
So without further adieu - why don't we (the collective group of musicians from around the world who are members of Music Stack Exchange) just all agree to call the collection of sharp symbols or flat symbols in the key signature "incidentals"!