Pitfalls for migration from apache php_module to fcgi?

I am working on a server with two WordPress sites (v5.9) and multiple other services. Everything is served with Apache (v2.4.6).

Now I am about to create a new PHP service, which should also being talked to via Apache. Therefore I would like to migrate from Apache php_module (PHP 7.2) to php_fpm and mod_proxy_fcgi.

There are plenty of tutorials and docs for both ways of using Apache, PHP and WordPress, but I did not see any hints for this kind of migration.

What do need to be aware of? Where are the pitfalls?

Here is my current Apache configuration

php.conf:

#
# The following lines prevent .user.ini files from being viewed by Web clients.
#
<Files ".user.ini">
    <IfModule mod_authz_core.c>
        Require all denied
    </IfModule>
    <IfModule !mod_authz_core.c>
        Order allow,deny
        Deny from all
        Satisfy All
    </IfModule>
</Files>

#
# Allow php to handle Multiviews
#
AddType text/html .php

#
# Add index.php to the list of files that will be served as directory
# indexes.
#
DirectoryIndex index.php

# mod_php options
<IfModule  mod_php7.c>
    #
    # Cause the PHP interpreter to handle files with a .php extension.
    #
    <FilesMatch \.(php|phar)$>
        SetHandler application/x-httpd-php
    </FilesMatch>

    #
    # Uncomment the following lines to allow PHP to pretty-print .phps
    # files as PHP source code:
    #
    #<FilesMatch \.phps$>
    #    SetHandler application/x-httpd-php-source
    #</FilesMatch>

    #
    # Apache specific PHP configuration options
    # those can be override in each configured vhost
    #
    php_value session.save_handler "files"
    php_value session.save_path    "/var/lib/php/session"
    php_value soap.wsdl_cache_dir  "/var/lib/php/wsdlcache"

    #php_value opcache.file_cache   "/var/lib/php/opcache"
</IfModule>

One of the WordPress sites as Apache Vhost:

<Ifmodule mod_ssl.c>

# Listen 443
<VirtualHost *:443>
    DocumentRoot "/var/www/wp-cockpit.de/"
    ServerName wp-cockpit.de
    ServerAlias www.wp-cockpit.de

    <Directory "/var/www/wp-cockpit.de/">
        Options Indexes FollowSymLinks
        AllowOverride All
        Require all granted
    </Directory>

    ErrorLog "/var/log/httpd/webServer-error_log"
    CustomLog "/var/log/httpd/webServer-access_log" combined

    SSLEngine on
    # SSLCertificateFile /etc/letsencrypt/live/co2-avatar.com/fullchain.pem
    
    SSLCertificateFile /etc/letsencrypt/live/co2-avatar.com/cert.pem
    SSLCertificateChainFile /etc/letsencrypt/live/co2-avatar.com/chain.pem
    SSLCertificateKeyFile /etc/letsencrypt/live/co2-avatar.com/privkey.pem
    
    Include /etc/letsencrypt/options-ssl-apache.conf

    #SSLCertificateFile /etc/letsencrypt/live/co2-avatar.com/fullchain.pem
    #SSLCertificateKeyFile /etc/letsencrypt/live/co2-avatar.com/privkey.pem
    # SSLCertificateChainFile /etc/letsencrypt/live/co2-avatar.com/chain.pem
</VirtualHost>
</IfModule>