Commands in Dockerfile has no effect in container (Docker) - laravel

Question

I am deploying dockerized application to digitalocean server. (Ubuntu 22.04)
But I don't want to pass vendor directory there. To create it in remote server I am trying to use composer update method in my application's container.
docker-compose.yml:
version: "3.9"
services:
#PHP Service
app:
build:
context: .
dockerfile: Dockerfile
image: digitalocean.com/php
container_name: app
restart: unless-stopped
tty: true
environment:
SERVICE_NAME: app
SERVICE_TAGS: dev
working_dir: /var/www
volumes:
- ./:/var/www
networks:
- app-network
#Nginx Service
webserver:
image: nginx:alpine
container_name: webserver
restart: unless-stopped
tty: true
ports:
- "80:80"
- "443:443"
volumes:
- ./:/var/www
- ./nginx/conf.d/:/etc/nginx/conf.d/
networks:
- app-network
#Docker Networks
networks:
app-network:
driver: bridge
Dockerfile:
FROM php:8.1-fpm as php
USER root
WORKDIR /var/www
# Install PHP packages
RUN apt-get update && apt-get install -y \
git \
curl \
libreoffice \
build-essential \
libpng-dev \
libjpeg62-turbo-dev \
libfreetype6-dev \
locales \
zip \
jpegoptim optipng pngquant gifsicle \
vim \
unzip \
libonig-dev \
libzip-dev
# Clear cache
RUN apt-get clean && rm -rf /var/lib/apt/lists/*
# Install extensions
RUN docker-php-ext-install mbstring zip exif pcntl
RUN docker-php-ext-configure gd --enable-gd --with-freetype=/usr/include/ --with-jpeg=/usr/include/
RUN docker-php-ext-install gd
# Copy existing application directory contents
COPY . /var/www
# Install composer
RUN curl -sS https://getcomposer.org/installer | php -- --install-dir=/usr/local/bin --filename=composer
RUN composer update
RUN composer dump-autoload
RUN chmod -R 755 storage/
# Expose port 9000 and start php-fpm server
EXPOSE 9000
CMD ["php-fpm"]
When I run docker build and up commands everything working fine without any error. But my application throws an error because it can't find vendor directory in application.
As you see in Dockerfile I am running composer update command. It is working while building and gives me some logs:
But when I log in my container with docker exec -it app /bin/bash command, I can't see any vendor directory created in /var/www. I am able to run composer update in container manually and it is not giving any error.
Main problem is why composer update is not creating vendor directory while givings logs. Even RUN chmod -R 755 storage/ command is not giving defined permissions to folder. I feel like Dockerfile has no effect on my container except installing packages and extensions.