The solution depends on what you're trying to accomplish with the right-click.
If you're trying to retrieve the source of the page
You can get it with page.content() easily, or you can use CDPSession to access Chrome's page.captureSnapshot
If you're trying to right-click a custom context menu which is coded in your app
Playwright doesn't support selecting options from Chrome's context menu, but when you say "I expect a different item," this tells me that your application may have a right-click handler which opens its own in-app context menu instead of Chrome's. In that case, you can locate and left-click on the element that is now visible as a result of your right-click.
Something like
await page.locator(".right-clickable-element").click( { button: "right" });
await page.locator(".app-custom-context-menu-option").click();
view-source:to your URL rather than right-clicking to view the source, although there's never really any reason for that since Playwright haspage.content(). You want to automate the page, not the browser that displays the page.