Hello,
Just to be sure, the folder where your logs are supposed to be written can be accessed by your server (on linux) ? I'm talking about access rights of the folders/files
You can find your current log folder path there :

filesconfigparameters.php

at the line with this parameter

$logFile=

The following line in ../files/config/parameters.php is :
$logFile='../files/logs/projeqtor_${date}.log';
(By default I think)

The access rights (for the log file?) :
../files/logs# ls -la
total 484
drwxr-xr-x 2 root root 4096 5 févr. 14:38 .
drwxr-xr-x 10 root root 4096 2 févr. 11:02 ..
-rw-r--r-- 1 root root 1256 2 févr. 11:02 index.php
-rw-r--r-- 1 root root 479107 2 févr. 11:51 projeqtor_20240202.log
-rw-r--r-- 1 root root 489 5 févr. 12:11 projeqtor_20240205.log

(Also don't know how to integrate lines code)

Rights are not correct : they are restricted to root user.
You should change ownership 

chown -R www-data: projeqtor/files

The chown worked, the strange part is i've done previously and it was pretty similar (chown -R www-data:www-data /var/www/projeqtor/)

Good point is that I'm progressing. A new error has appeared :
mbstring module not enabled (mb_check_encoding not existing) : install module and unable module in php.ini

Do you know where to get this "module" ?

Google is your friend

Sorry Snitnil, but we only provide a free support for ProjeQtOr on this forum, not the full installation of your own web server on Linux. You can find many help on the internet about this.

Sorry I'm not very comfortable with going so far in a website configuration. I thought it was still closely related to projeqtor. I'm gonna search by myself about this for now and if I find a solution to this problem in particular, I will come and give the answer to potentially help people that would also be affected

I did some research and it turns out that the basic packages for the LAMP server are not sufficient.
The modules I was missing were related to php. So here are all the packages to install for a LAMP server which will host the projeqtor tool: curl, apache2, php, libapache2-mod-php, php-mysql, php-mbstring, php-xml, php-zip, mariadb-server .

(I was also wondering if I could include a drive link to my documentation for this project?)

Hello,
Glad you found out what you need to install in order to make your local webserver run correctly.
Just in case, have you read our technical prerequisites where most of these modules are indeed listed as required or recommended ?

Ok thank you. I hadn't paid attention to this section but rather to the "Setup and Migration" section. A link to this page was sent to me so I didn't pay attention to the details :/
Once again, sorry and thank you for your time and attention.