How can I configure my IDE to automatically use the authenticated user's remote username and email for local GIT

How can I automate setting the local Git username and email in IntelliJ IDEA and PhpStorm when using Git over HTTPS to match the remote credentials after authentication?

Local git user.name and user.email values are used for putting author information in commits, not for authenticating to remote repositories. So those two are not really related.

I've been testing Git with Gitea and OneDev and encountered a username discrepancy between the website's author and the IDE's local user, even though I've used the same remote credentials for authentication. 

Could you please elaborate on this a bit more? What kind of issue did you encounter? Did you get an error message?

What's the standard practice for ensuring accurate commit and push authorship in larger organizations? 

The best way is to run following git commands to set the user.name and user.email values in your global git configuration. This way for every repository that you clone, git will use this username and email. Just replace the placeholders with your actual name and email.

git config --global user.name "FIRST_NAME LAST_NAME"
git config --global user.email "email@domain.com"

Additionally, I'd like to know how to configure Git in my IDE to automatically use the authenticated user's remote username and email to streamline this process. 

IntelliJ relies on command line git, and git user name/email  is determined by the git config. It is not saved in the IDE.
IDE invokes local git commands, as if you are running them via command line (git bash). Also, git by itself doesn't support this functionality out-of-the-box. However, you can check this SO comment for an alternative approach: https://stackoverflow.com/a/63758005/21118454.

Also, you should consider using SSH to authenticate to remote repositories, instead of HTTPS. It is much easier to use as you don't need to worry about supplying credentials when issuing git commands. Git uses preconfigured SSH keys to authenticate automatically.