You should install the development support files for zlib, try:

sudo apt-get install libz-dev

^{Other package names: zlib1g-dev.}

If you've already zlib library, make sure you're compiling your code sources with -lz. See: missing zlib.h in ubuntu.

Install zlib with development support by using

sudo apt-get install zlib1g-dev

In case you don't want or need to use the full zlib, it is fairly easy to write wrapper routines which map the zlib functions 1:1 to ordinary file functions which don't support compression and decompression.

//
//  dummy zlib.h
//

#pragma once
#include <stdio.h>

typedef FILE *gzFile;

int gzclose(gzFile file);
gzFile gzdopen(int fd, const char *mode);
gzFile gzopen(const char *path, const char *mode);
int gzread(gzFile file, void *buf, unsigned int len);


//
//  zlibDummy.cpp
//

#include <zlib.h>

int gzclose(gzFile file)
{
    return fclose(file);
}

gzFile gzdopen(int fd, const char *mode)
{
    return _fdopen(fd, mode);
}

gzFile gzopen(const char *path, const char *mode)
{
    return fopen(path, mode);
}

int gzread(gzFile file, void *buf, unsigned int len)
{
    return fread(buf, 1, len, file);
}

Seems compiler is not able to find the file in the includes path you mentioned.
First check if zconf.h file is available on your machine and get that location. If the file is available then just give the path of the file to the compiler using -I option.

INCLUDE = -I"<YourPath>" -I"./src/" -I"/usr/include/" -I"$(CODEBASE)/seqlib/src/libs/seqan-library-2.0.1/include" -I"$(CODEBASE)/seqlib/src/libs/libdivsufsort-2.0.1-64bit/" $(CODEBASE_SRC_FOLDERS)

If the file itself is missing, then you would need to install it

sudo apt-get install libz-dev

Based on information shared by @Knud Larsen :
The Ubuntu package name is zlib1g-dev from where you can get the missing file. /usr/include/zconf.h
https://packages.ubuntu.com/focal-updates/amd64/zlib1g-dev/filelist