Hi !
Ok, Here are all the answers to your list 
Full path : /home/lexa5522/crm2024leparc/
inside this root folder for the CRM, I have all the folders (bin, cache, config, core, extensions, logs, public, tmp, vendor) and several file of the crm (.editorconfig, .env, .env.local, .eslintrc.js, angular.json, composer.lock, files.md5, LICENCE.txt, package.json, proxy.conf.env.json, README.md, symfony.lock, tsconfig.json, tslint.json, VERSION, yarn.lock). I also add here an empty index.html to avoid listings.
APACHE : the one used on host O2switch, I dont know the version used.
PHP : 8.1
Type and version MariaDB : 10.6.16-MariaDB - type Mysql
Htaccess file : only in the folder public, the content of the .htaccess is :
# Use the front controller as index file. It serves as a fallback solution when
# every other rewrite/redirect fails (e.g. in an aliased environment without
# mod_rewrite). Additionally, this reduces the matching process for the
# start page (path "/") because otherwise Apache will apply the rewriting rules
# to each configured DirectoryIndex file (e.g. index.php, index.html, index.pl).
DirectoryIndex index.php
# By default, Apache does not evaluate symbolic links if you did not enable this
# feature in your server configuration. Uncomment the following line if you
# install assets as symlinks or if you experience problems related to symlinks
# when compiling LESS/Sass/CoffeScript assets.
# Options FollowSymlinks
# Disabling MultiViews prevents unwanted negotiation, e.g. "/index" should not resolve
# to the front controller "/index.php" but be rewritten to "/index.php/index".
<IfModule mod_negotiation.c>
Options -MultiViews
</IfModule>
<IfModule mod_rewrite.c>
RewriteEngine On
RewriteRule ^index.php.*$ - [L,NC]
# Determine the RewriteBase automatically and set it as environment variable.
# If you are using Apache aliases to do mass virtual hosting or installed the
# project in a subdirectory, the base path will be prepended to allow proper
# resolution of the index.php file and to redirect to the correct URI. It will
# work in environments without path prefix as well, providing a safe, one-size
# fits all solution. But as you do not need it in this case, you can comment
# the following 2 lines to eliminate the overhead.
RewriteCond %{REQUEST_URI}::$0 ^(/.+)/(.*)::\2$
RewriteRule .* - [E=BASE:%1]
# Sets the HTTP_AUTHORIZATION header removed by Apache
RewriteCond %{HTTP:Authorization} .+
RewriteRule ^ - [E=HTTP_AUTHORIZATION:%0]
# Redirect to URI without front controller to prevent duplicate content
# (with and without `/index.php`). Only do this redirect on the initial
# rewrite by Apache and not on subsequent cycles. Otherwise we would get an
# endless redirect loop (request -> rewrite to front controller ->
# redirect -> request -> ...).
# So in case you get a "too many redirects" error or you always get redirected
# to the start page because your Apache does not expose the REDIRECT_STATUS
# environment variable, you have 2 choices:
# - disable this feature by commenting the following 2 lines or
# - use Apache >= 2.3.9 and replace all L flags by END flags and remove the
# following RewriteCond (best solution)
RewriteCond %{ENV:REDIRECT_STATUS} =""
RewriteRule ^index\.php(?:/(.*)|$) %{ENV:BASE}/$1 [R=301,L]
# If the requested filename exists, simply serve it.
# We only want to let Apache serve files and not directories.
# Rewrite all other queries to the front controller.
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^ %{ENV:BASE}/index.php [L]
</IfModule>
<IfModule !mod_rewrite.c>
<IfModule mod_alias.c>
# When mod_rewrite is not available, we instruct a temporary redirect of
# the start page to the front controller explicitly so that the website
# and the generated links can still be used.
RedirectMatch 307 ^/$ /index.php/
# RedirectTemp cannot be used instead
</IfModule>
</IfModule>
The CRM is running on a subdomain (as before on the V8.4.0, no change),
The VirtualHost in CPanel is pointing the subdomain directly on the folder : mysubdomain.mydomain.com → /crm2024leparc
It is here where I tried to add /public at the end : this working but this also break some part of the CRM like the url for images used in PDF for example.
Nothing in suitecrm.log related to this (only some warning linked to imap).
Do you see anything wrong ?
Thanks
Xavier
this (adding public at the end) is correct. You should leave it like that and try to solve the other problems that arise.