Do Assistants Run on local or OpenAI infrastructure

I am confused and hope someone can provide clarity for me.

I have a curated OpenAI Vector Store which contains document chunks from documents located in OpenAI File store.

each chunk includes a meta reference to the document in the file store.

My .net Client App captures the users prompt as audio message.

I would like my assistant to first transcribe the incoming audio message to text transcription and send web socket message back to the client including the transcribed text and language.
The assistant then would transform the transcription into a vector embedding set that is then queried against the Vector Store, returning the top matches.
extract the related Document Id and retrieve all related documents.
then publish the list of document Ids for each document matched.
then perform a final AI assessment of the question, the conversation history and the documents matched plus related system instructions and returns the response back to the client.

Can these steps all run in the Assistant or do I run these on the client, invoking API calls into OpenAI? ChatGpt says this is all orchestrated from the client not on OpenAI but the model is from last year so I’m not sure its aware of assistants.

Are there any similar examples ?

note: I have this running all on the client but was thinking it would be more performant if run as an assistant on OpenAI.