A word for the experience and vernacular of a group of people - Discord? Is this correct?

You have definitely misremembered the word. The Merriam Webster definitions of discord as a noun are:

1 a: lack of agreement or harmony (as between persons, things, or ideas)

1 b: active quarreling or conflict resulting from discord among persons or factions : STRIFE

2 a music (1): a combination of musical sounds that strikes the ear harshly (2): DISSONANCE

b: a harsh or unpleasant sound

It also gives a definition as an intransitive verb:

Disagree or clash

I am struggling to think what the original word might be, but it certainly is not discord

EDIT: I've had another think and believe that the original word may gave been discourse

Merriam Webster gives five definitions of dicourse as a noun and two as a verb but the most relevant to your question is number 3:

a mode of organizing knowledge, ideas, or experience that is rooted in language and its concrete contexts (such as history or institutions)

I find the use of discourse a little odd in the context you give but it certainly makes more sense than discord and is sufficiently similar in spelling and pronunciation for the words to be confused in long term memory.

"Discourse" is probably the word. [As BoldBen and Anton have said since I started typing!]

Your definition "the collection of vernacular and experiences of a group of people" isn't far off the mark, and I think the word is being used more loosely today than Lexico's definitions suggest. In fact it's so popular it sometimes appears where "conversation", "language" or even "chit-chat" might have been used in the past!

I think if you look at Lexico's examples of its usage, and perhaps Google it to see how it's being used, you might decide if it's the missing word.

For instance, a programmer might use the phrase "assembly". The layman might think they mean a group of people, but they were actually talking about the computer language.

I believe the term for this is jargon:

1: the technical terminology or characteristic idiom of a special activity or group

If I recall correctly from school, jargon doesn't need to be new words per se, but can be vocation or other in-group related slang.