It will be faster to open Jira issues that are mentioned in Github commit messages or pull requests with one click.
This feature is called autolinking or "Autolinks to reference external resources".
You can configure this on the repository level only (at this stage).
When you click Add autolink reference you can enter your Jira details as below
And the issue keys in commit messages transform into links.
As well as the links in the PR description transform as well.
If you want to autolink items in Jira to reference GitHub pull requests, repositories, users, organizations, issues, etc you can use Github Links for Jira (or Confluence).
Useful links are:
Github Links for Confluence app available on Atlassian Marketplace.