Why it is showing "no repository found" in vs-code (using CLI for github), into my project?

Question

I am making a front-end of a project for an organization. The organization has a very first project related to a software, so they created a GitHub organization account, where they created the GitHub repository, under the same name as "one of the project of the organization".

They have made me the member who could possibly contribute the code to the organisation repositories. The manager has added two usernames, as their member:

1. front-end, i.e me
2. backend, i.e, the person's username who is writing the backend of this project.

Now, I have prepared the front-end of a project, using create-react-app (CRA). My src folder size is hardly 1 MB, as I have already coded a lot, whilst my overall application size is coming out to be more then 2.55 GB.

Problem : I tried to access the organization's repository using my Terminal and CLI in vs.code.

I have following [remote origins] into my GitHub (kindly, please note that I have a different username which is added as a member of the Organization I am working on, and currently, I am being signed in with that username (my official One), over the GitHub).

So, when I run the command into the MAC Terminal,

$ git remote show

I have seen that following remote origins are there ,

 - My_Organisation
 - My_Front_End_project_in_org
 - origin
 - Organisation_origin

I have prepared the code, and staged & committed using the source control in VS_CODE. Now Once committed and staged, I am getting the message: Publish Branch. My current branch is main, I have confirmed in VS_Code bottom taskbar.

Now, when I tried to view any of the origin over my Terminal using the command,

 $ git remote show My_Organisation

the result logs are showing me -

remote: Repository not found.

fatal : repository https://github.com/My-organisation-name/my_projectname.git" not found.

Although, I could access the organization's repository, from my account (used to register inside the organization over the GitHub). Plus: The organization has the PRIVATE repository.

I think maybe because of the fact that the repository is PRIVATE in nature. my VS_Code is not able to detect the repository, and giving me the "repository not-found error message"!

When I use source control into my vs-code and adopt the following procedure, to push the code to GitHub, inside of my organization's repository

1. Staging all the changes I made in code by clicking '+' icon, right over all the files in source control tab.
2. Writing a commit message "ABC_Feature_Added" , and commiting the changes
3. Going to '...' icon, and selecting pull/push -> push to -> then selecting my remote origin repository, where I want to push the code changes to. -- Here I am getting the prompt as "remote origin not-found" from VSCode.

I am very new to GITHUB, and haven't used/seen others using this much, but it is a vital part of any developer's career/organization's growth.

I couldn't say, whether the organization has forked the branch or not. My problem is, every time I tries to push the committed changes to the repository, into my organization's account, I am getting error - "Remote repository not found". What am I doing wrong, how should I solve this issue?

I am new to this job, and learning GitHub, almost as a beginner, and the company wants me to push the code ASAP to the organization's repository.

My overall project size is 2.55 GB. This much enormous size is because of many node_modules files, I am making use of as per organization's project needs.

How can I successfully upload everything (all code + images +_ all folders) to this repository under the organization?

Plus, the organization has a PRIVATE repository, but I am granted as the "member" access inside the organization account on GitHub?