Create 2 JIRA classic scheme projects and 1 JIRA Agile project and consider below 3 cases:

#1. When, using Top Nav Project drop down list I switch between two of mine JIRA classic projects, ProjectKey/Id is refreshed in my hyperlinks. Please refer to screenshot "Links with JIRA classic projects.png"

#2. But when I switch from a JIRA classic project to JIRA Agile project, ProjectKey/Id is not updated in my hyperlinks. Please refer to screenshot "Links with JIRA Agile project wrong project key.png".

#3. After selecting agile project, if I refresh the screen, I can see the right ProjectKey/Id in my links.
Please refer to screenshot "Links with JIRA Agile project right project key.png".

Essentially, while I switch between non-agile projects these links are updated with selected ProjectKey/Id. But when I switch from a non-agile project to an agile project, ProjectKey/Id is not updated until I refresh the screen.