Excecute .sh file on start of Docker container and let container run - shell

Question

I have a docker container that serves a webserver. On every startup of the container, I want to excecute a little shell script. The script that has to be executed has only one statement.
/var/www/html/app/Console/cake schema update -y
To achieve this, I created a .sh file called schemaupdate.sh which I copy into the docker container using the dockerfile into the /etc/init.d folder. Furthermore I make it executable and register it to the startup.
COPY schemaupdate.sh /etc/init.d/schemaupdate.sh
chmod 755 /etc/init.d/schemaupdate.sh
update-rc.d schemaupdate.sh defaults
The file is successfully copied into the container. However, the script is not executed when the docker container starts. When I manually call the sh file, everything is running fine.
How can I achieve, that the file / statement is executed on each startup of a container? It is important, that the script is executed at the startup and the container (so the webserver) still continues to run! The script only makes a little update check and after the check the webserver keeps on going.
The container is a debian based container. Here is inital dockerfile.
#start with base Image from php
FROM php:7.3-apache
#install system dependencies and enable PHP modules
RUN apt-get update && apt-get install -y \
libicu-dev \
libpq-dev \
libmcrypt-dev \
mysql-client \
git \
zip \
unzip \
&& rm -r /var/lib/apt/lists/* \
&& docker-php-ext-configure pdo_mysql --with-pdo-mysql=mysqlnd \
&& docker-php-ext-install \
intl \
mbstring \
pcntl \
pdo_mysql \
pdo_pgsql \
pgsql \
opcache
# zip \
# mcrypt \
#configure imap for mails
RUN apt-get update && \
apt-get install -y \
libc-client-dev libkrb5-dev && \
rm -r /var/lib/apt/lists/*
RUN docker-php-ext-configure imap --with-kerberos --with-imap-ssl && \
docker-php-ext-install -j$(nproc) imap
#install mcrypt
RUN apt-get update \
&& apt-get install -y libmcrypt-dev \
&& rm -rf /var/lib/apt/lists/* \
&& pecl install mcrypt-1.0.2 \
&& docker-php-ext-enable mcrypt
#install composer
RUN curl -sS https://getcomposer.org/installer | php -- --install-dir=/usr/bin/ --filename=composer
#set our application folder as an environment variable
ENV APP_HOME /var/www/html
#change uid and gid of apache to docker user uid/gid
RUN usermod -u 1000 www-data && groupmod -g 1000 www-data
#change the web_root to cakephp /var/www/html/webroot folder
#RUN sed -i -e "s/html/html\/webroot/g" /etc/apache2/sites-enabled/000-default.conf
# enable apache module rewrite
RUN a2enmod rewrite
#copy source files and run composer
#COPY src/ /var/www/html
#COPY src/ $APP_HOME
# install all PHP dependencies
#RUN composer install --no-interaction
#SET Volume
VOLUME /var/www/html/
#change ownership of our applications
RUN chown -R www-data:www-data $APP_HOME
#SET ENV VARIABLES
COPY schemaupdate.sh /etc/init.d/schemaupdate.sh
chmod 755 /etc/init.d/schemaupdate.sh
update-rc.d schemaupdate.sh defaults
EXPOSE 80

Answer 1

/etc/init.d/ isn't relevant. Containers aren't full blown operating systems with a heavyweight SysV init-style startup sequence. They run a single command, that's it.
You should either add the command as a RUN statement in the Dockerfile so its results are baked into the image, or you should have it called directly by the container's CMD or ENTRYPOINT directive.

Answer 2

I Finally used the Entrypoint. I deleted the COPY, chmod and update-rc. The Entrypoint looks like the following.
ENTRYPOINT [ "sh", "-c", "/var/www/html/app/Console/cake schema update -y && /var/www/html/app/Console/cake schema update -y && /usr/sbin/apachectl -D FOREGROUND"]
It first starts the update statment. After this is finished (so terminated), the apachectl is called to keep the webserver running.