pkg-config: Requires problem: ld cannot find file - gcc

Question

I have a library which until now was just a static library, and I used it as a submodule of my programs.
Now I want to be able to install it and be able to use it both as a static and a shared library.
I installed (apart from the header files) the following files:
$ tree /usr/local/lib/
/usr/local/lib/
├── libalx
│   ├── libalx-base.a
│   ├── libalx-base.so
│   ├── libalx-cv.a
│   ├── libalx-cv.so
│   ├── libalx-gsl.a
│   ├── libalx-gsl.so
│   ├── libalx-ncurses.a
│   ├── libalx-ncurses.so
│   ├── libalx-ocr.a
│   └── libalx-ocr.so
├── pkgconfig
│   ├── libalx-base.pc
│   ├── libalx-cv.pc
│   ├── libalx-gsl.pc
│   ├── libalx-ncurses.pc
│   └── libalx-ocr.pc
The contents of (some of) the pkg-config files are the following:
libalx-base.pc:
Name: libalx-base
Description: The libalx C/C++ library (base module)
URL: https://github.com/alejandro-colomar/libalx
Version: 1~b4
Requires: libbsd-overlay
Requires.private:
prefix=/usr/local/
libdir=${prefix}/lib/
Cflags: -D _GNU_SOURCE -D _POSIX_C_SOURCE=200809L
Libs: -L ${libdir}/libalx/ -l alx-base
libalx-cv.pc:
Name: libalx-cv
Description: The libalx C/C++ library (openCV extension)
URL: https://github.com/alejandro-colomar/libalx
Version: 1~b4
Requires: libalx-gsl
Requires.private: opencv libalx-base
prefix=/usr/local/
libdir=${prefix}/lib/
Cflags: -D _GNU_SOURCE -D _POSIX_C_SOURCE=200809L
Libs: -L ${libdir}/libalx/ -l alx-cv
libalx-gsl.pc:
Name: libalx-gsl
Description: The libalx C/C++ library (GSL extension)
URL: https://github.com/alejandro-colomar/libalx
Version: 1~b4
Requires:
Requires.private: gsl libalx-base
prefix=/usr/local/
libdir=${prefix}/lib/
Cflags: -D _GNU_SOURCE -D _POSIX_C_SOURCE=200809L
Libs: -L ${libdir}/libalx/ -l alx-gsl
I'm using the library in a program that makes use of only two of the modules: base & cv.
I use the following CFLAGS and LIBS (LDFLAGS) in its Makefile:
################################################################################
# cflags
CFLAGS_STD = -std=gnu17
CFLAGS_OPT = -O3
CFLAGS_OPT += -march=native
CFLAGS_OPT += -flto
CFLAGS_W = -Wall
CFLAGS_W += -Wextra
CFLAGS_W += -Wstrict-prototypes
CFLAGS_W += -Werror
CFLAGS_PKG = `pkg-config --cflags opencv`
CFLAGS_PKG += `pkg-config --cflags libalx-cv`
CFLAGS_PKG += `pkg-config --cflags libalx-base`
CFLAGS_D = -D PROG_VERSION=\"$(PROGRAMVERSION)\"
CFLAGS_D += -D INSTALL_SHARE_DIR=\"$(INSTALL_SHARE_DIR)\"
CFLAGS_D += -D INSTALL_VAR_DIR=\"$(INSTALL_VAR_DIR)\"
CFLAGS = $(CFLAGS_STD)
CFLAGS += $(CFLAGS_OPT)
CFLAGS += $(CFLAGS_W)
CFLAGS += $(CFLAGS_PKG)
CFLAGS += $(CFLAGS_D)
export CFLAGS
################################################################################
# libs
LIBS_OPT = -O3
LIBS_OPT += -march=native
LIBS_OPT += -flto
LIBS_OPT += -fuse-linker-plugin
LIBS_PKG = `pkg-config --libs libalx-cv`
LIBS_PKG += `pkg-config --libs libalx-base`
LIBS = $(LIBS_OPT)
LIBS += $(LIBS_PKG)
export LIBS
################################################################################
And I have the following error:
gcc tmp/coins.o tmp/main.o tmp/parse.o -o cv-coins -O3 -march=native -flto -fuse-linker-plugin `pkg-config --libs libalx-cv` `pkg-config --libs libalx-base`
/usr/bin/ld: cannot find /usr/local//lib//libalx/: file format not recognized
collect2: error: ld returned 1 exit status
What is wrong? I assume the problem is in the .pc files, but I tried moving dependencies from requires to requires.private, the other way around, and other things, and none worked. For example, if I move libbsd-overlay to Requires.private, then the linker complains about not finding strnstr.