Yes you will have to show those third party notices.
If you include components into your software, you (and you alone) are responsible for complying with the licenses of those components. It doesn't matter here whether you included those components manually, or whether they were transitive dependencies.
Of course the state of license compliance is … not good. Many software developers are not aware of their license obligations. However, "everyone else is doing it" isn't a valid defense.
The Godot manual explicitly calls out the need to show certain third party license notices. The Unreal Engine licensing terms also mention the need to comply with third party licenses, and explains where to find their licenses.
Showing these licenses doesn't require excessive effort and doesn't have to result in awful user experience. Many professional apps have a menu entry that leads to a screen that contains all licenses, perhaps made easier to navigate via an accordion user interface. Some package managers like JavaScript's Yarn have built-in tools for generating such pages. Wherever you assert your own copyright in the application, also mention that some copyright is held by third parties, and link to that license notice page.
Being aware of all the licenses of all components can be helpful in case there are surprising license terms in there. While all Open Source licenses allow you to use, modify, and share the software for any purpose, there might be unusual notice terms, patent clauses, or copyleft mechanisms. I therefore think that it is sensible for a professional project to allowlist acceptable licenses, and to have an automated check during the build process to verify that no surprising licenses snuck in.