> Is the license (MPL) of Eigen compatible with the GPLv3+ license?
> If I use Eigen, I need it to be compiled (using GCC 13 -with on Debian/Trixie/x86-64) with both optimization flags and DWARF debugging information.
Eigen is header-only, you can compile your own code however you need.
> Is the Eigen library POSIX thread friendly?
Core Eigen is single-threaded, unless you enable OpenMP. The Tensor module has a std::thread-based threadpool, which, yes, is compatible.
> Is the Eigen library compilable easily (on a Linux/x86-64 desktop or laptop) with GCC 13 using -standard=gnu17 -Wall -Wextra -O -g -fPIE ? How to do that easily? (I don't know much about cmake, and prefer GNU make)
You don't need to use cmake. It's header only, so just ensure it's in your header search path and compile however you like.
~Antonio