Limit php-fpm to a specific sub directory generally handled by apache

Question

I am facing the following legacy setup with php-7.4 and libapache2-mod-php7.4 installed and enabled:

<VirtualHost *:80>
    ServerName example.com
    DocumentRoot /var/www/html

    <Directory /var/www/html>
        Options FollowSymLinks
        AllowOverride All
    </Directory>

    ErrorLog ${APACHE_LOG_DIR}/error.log
    CustomLog ${APACHE_LOG_DIR}/access.log combined
</VirtualHost>

• /var/www/html/project1 -> Apache 2.0 Handler / PHP 7.4 -> example.com/project1
• /var/www/html/project2 -> Apache 2.0 Handler / PHP 7.4 -> example.com/project2

I am new to the company and I now have to implement /var/www/html/project3, accessible via example.com/project3. The legacy projects are not able to run on recent PHP versions but I like to run project3 with recent PHP 8.2. Therefore I thought of installing php8.2-fpm and let Apache handle just the requests to /var/www/html/project3 via SetHandler [...]php8.2-fpm.sock.

See in the comments of the above snippet how I tried to achieve this without success:

<VirtualHost *:80>
    ServerName example.com
    DocumentRoot /var/www/html

    # This works, but sets php8.2-fpm globally for the whole /var/www/html directory
    # this breaks project1 and project2
    <FilesMatch \.php$>
        SetHandler proxy:unix:/var/run/php/php8.2-fpm.sock|fcgi://dummy
    </FilesMatch>

    # This has no effect at all (but I guess my intent is clear)
    <Directory /var/www/html/project3>
        <FilesMatch \.php$>
            SetHandler proxy:unix:/var/run/php/php8.2-fpm.sock|fcgi://dummy
        </FilesMatch>
    </Directory>

    <Directory /var/www/html>
        Options FollowSymLinks
        AllowOverride All
    </Directory>

    ErrorLog ${APACHE_LOG_DIR}/error.log
    CustomLog ${APACHE_LOG_DIR}/access.log combined
</VirtualHost>

I thought of using another VirtualHost with different DocumentRoot, but I have two requirements that made me believe I have to use the same VirtualHost as for the legacy projects:

1. the final URL has to be of the same kind as for the legacy projects (example.com/project3)
2. due to CI/CD, the project's location must be /var/www/html/project3. The only thing I can do is placing a symlink somewhere else in the file system

So if you either have an idea how to solve this in the existing VirtualHost defintion or can help me with a solution for a second VirtualHost that satisfies the two requirements + sets the php-fpm handler, I would greatly appreciate.