The right-click context menu in Cursor’s browser shows link-specific options (like “Open in New Tab” or “Copy Link Address”) only when right-clicking a standard HTML link. MCP tool results – like the Jira cards from the Atlassian integration shown in your screenshot – render their own custom elements, so the right-click menu won’t include link options for those. The “Open link” icon on each card is the intended way to open those links.
This is related to your earlier thread about link handling in the Agents View. The broader ability to choose between internal and external browser for links is something the team is aware of and working on improving.