It is said that layer 3 devices such as routers do not have an
No, routers route at layer-3, not the application layer, but that does not mean a router cannot have a user interface in the application layer.
But whenever I want to configure my home router I punch in the IP
address and open up its graphical user interface.
Home networking and consumer-grade devices are explicitly off-topic here.
What should we call that type of "applications" of such low level devices?
Such a user interface is an application. A PC is also a layer-3 device, but it can run applications. A router is also a host, like a PC, and, in fact, a routing protocol (exchanges routing information between routers, but does not actually route) is an application.
"Importantly, you do not need to write software that runs on
network-core devices, such as routers or link-layer switches. Even if
you wanted to write application software for these network-core
devices, you wouldn’t be able to do so." Computer networking a top
down approach by James Kurose
That is because most enterprise-grade devices run a proprietary OS for which you have no way to write an application, although the manufacturer can and does write applications for its devices. This is changing a bit, e.g. Cisco has some OSes for which you can write applications under certain circumstances with certain restrictions, but the router process is run as a separate, proprietary process.