No, you do not have to recompile all installed applications after recompiling the Linux kernel.
When you recompile the Linux kernel, you are essentially creating a new kernel image file that contains the new kernel code and configuration options. This new kernel image file is then used when the system boots up.
Most user-level applications in Linux are not directly dependent on the kernel image file. Instead, they interact with the kernel through system calls, which are a set of functions provided by the kernel to access its services. As long as the new kernel image file is compatible with the existing system call interface, most user-level applications should continue to work without any issues.
However, there are some exceptions. Applications that have kernel modules or device drivers may need to be recompiled to be compatible with the new kernel image file. This is because kernel modules and device drivers are tightly coupled with the kernel and may not work correctly with a different kernel version.
Additionally, if you have custom-built applications that are compiled with specific kernel features or settings, you may need to recompile them to ensure compatibility with the new kernel.
In general, it is a good practice to test any custom-built or critical applications after a kernel recompile to ensure that they are still functioning correctly.