Problem with Makefile recompile library file each time - makefile

Question

Hello I am trying to lean make by following a makefile template in this repo
It is a project template to build for stm32f407 microcontroller. I have modified the makefile to include some standard library.
For time and resource saving, the standard library from the vendor should not be recompiled every time I run make. However, it is doing what I don't want it to do.
I am a novice about makefile.
Please take a look at my file and point me to the direction how should I fix it.
# Name of the binaries.
PROJ_NAME=project-template
######################################################################
# SETUP TOOLS #
######################################################################
# This is the path to the toolchain
# (we don't put our toolchain on $PATH to keep the system clean)
TOOLS_DIR = ../toolchain/bin
# The tools we use
CC = $(TOOLS_DIR)/arm-none-eabi-gcc
OBJCOPY = $(TOOLS_DIR)/arm-none-eabi-objcopy
GDB = $(TOOLS_DIR)/arm-none-eabi-gdb
AS = $(TOOLS_DIR)/arm-none-eabi-as
## Preprocessor options
# directories to be searched for header files
INCLUDE = $(addprefix -I,$(INC_DIRS))
# #defines needed when working with the STM library
DEFS = -DUSE_STDPERIPH_DRIVER
# if you use the following option, you must implement the function
# assert_failed(uint8_t* file, uint32_t line)
# because it is conditionally used in the library
# DEFS += -DUSE_FULL_ASSERT
##### Assembler options
AFLAGS = -mcpu=cortex-m4
AFLAGS += -mthumb
AFLAGS += -mthumb-interwork
AFLAGS += -mlittle-endian
AFLAGS += -mfloat-abi=hard
AFLAGS += -mfpu=fpv4-sp-d16
## Compiler options
CFLAGS = -ggdb
# please do not optimize anything because we are debugging
CFLAGS += -O0
CFLAGS += -Wall -Wextra -Warray-bounds
CFLAGS += $(AFLAGS)
## Linker options
# tell ld which linker file to use
# (this file is in the current directory)
LFLAGS = -Tstm32_flash.ld
######################################################################
# SETUP SOURCES #
######################################################################
# This is the directory containing the firmware package,
# the unzipped folder downloaded from here:
# http://www.st.com/web/en/catalog/tools/PF257904
STM_ROOT =../stlib
# This is where the source files are located,
# which are not in the current directory
# (the sources of the standard peripheral library, which we use)
# see also "info:/make/Selective Search" in Konqueror
MY_SRC_DIR = src
STM_SRC_DIR = $(STM_ROOT)/Libraries/STM32F4xx_StdPeriph_Driver/src
STM_SRC_DIR += $(STM_ROOT)/Utilities/STM32F4-Discovery
STM_STARTUP_DIR += $(STM_ROOT)/Libraries/CMSIS/ST/STM32F4xx/Source/Templates/TrueSTUDIO
# Tell make to look in that folder if it cannot find a source
# in the current directory
vpath %.c $(MY_SRC_DIR)
vpath %.c $(STM_SRC_DIR)
vpath %.s $(STM_STARTUP_DIR)
################################################################################
# SETUP HEADER FILES #
################################################################################
# The header files we use are located here
INC_DIRS = ./headers
INC_DIRS += $(STM_ROOT)/Utilities/STM32F4-Discovery/
INC_DIRS += $(STM_ROOT)/Libraries/CMSIS/Include/
INC_DIRS += $(STM_ROOT)/Libraries/CMSIS/ST/STM32F4xx/Include/
INC_DIRS += $(STM_ROOT)/Libraries/STM32F4xx_StdPeriph_Driver/inc/
################################################################################
# SOURCE FILES TO COMPILE #
################################################################################
# My source files
SRCS = main.c
# Contains initialisation code and must be compiled into
# our project. This file is in the current directory and
# was writen by ST.
SRCS += system_stm32f4xx.c
# Contain peripheral library source file
SRCS += stm32f4xx_vectors.c
SRCS += misc.c
SRCS += stm32f4_discovery.c
SRCS += stm32f4xx_rcc.c
SRCS += stm32f4xx_gpio.c
SRCS += stm32f4xx_syscfg.c
SRCS += stm32f4xx_exti.c
SRCS += systick.c
# Startup file written by ST
# The assembly code in this file is the first one to be
# executed. Normally you do not change this file.
ASRC = startup_stm32f4xx.s
# in case we have to many sources and don't want
# to compile all sources every time
OBJS := $(SRCS:.c=.o)
OBJS += $(ASRC:.s=.o)
######################################################################
# SETUP TARGETS #
######################################################################
TEMP_DIR = ./temp
OUT_DIR = ./out
.PHONY: all
all: $(PROJ_NAME).elf
%.o : %.c
#echo "[Compiling ] $^"
#mkdir -p ${TEMP_DIR}
#$(CC) -c -o $(TEMP_DIR)/$# $(INCLUDE) $(DEFS) $(CFLAGS) $^
%.o : %.s
#echo "[Assembling ] $^"
#mkdir -p ${TEMP_DIR}
#$(AS) $(AFLAGS) $< -o $(TEMP_DIR)/$#
$(PROJ_NAME).elf: $(OBJS)
#echo "[Linking ] $#"
#mkdir -p ${OUT_DIR}
#$(CC) $(CFLAGS) $(LFLAGS) $(foreach file, $^, $(TEMP_DIR)/$(file)) -o $(OUT_DIR)/$#
#$(OBJCOPY) -O ihex $(OUT_DIR)/$(PROJ_NAME).elf $(OUT_DIR)/$(PROJ_NAME).hex
#$(OBJCOPY) -O binary $(OUT_DIR)/$(PROJ_NAME).elf $(OUT_DIR)/$(PROJ_NAME).bin
clean:
#rm -f *.o $(OUT_DIR)/* $(TEMP_DIR)/*
flash: all
st-flash write $(OUT_DIR)/$(PROJ_NAME).bin 0x8000000
debug:
# before you start gdb, you must start st-util
$(GDB) -tui $(OUT_DIR)/$(PROJ_NAME).elf
Here is the picture of the command line
Thank you