Looking at your error message i come to the conclusion that you are trying to install a plugin or update wordpress itself

This issue is slightly tricky to figure out.

executing chown -R www-data:www-data /var/www to set correct user:group permissions should technically solve it, however ..

On a new wordpress install the upload & plugins folder does not yet exist and therefore when installer trying to create a plugins/subfolder it will throw the error.

How to Fix Wordpress / Docker Plugin install Permission issue

Fixing this issue is however quite easy once grasping it.

Option A

in your .Docker file add following towards the very end but before any [CMD] command.

RUN mkdir /var/www/html/wp-content/plugins
RUN mkdir /var/www/html/wp-content/uploads
RUN chown -R www-data:www-data /var/www
RUN find /var/www/ -type d -exec chmod 0755 {} \;
RUN find /var/www/ -type f -exec chmod 644 {} \;

Option B

ssh in to your docker container
docker exec -it <container_name> /bin/bash

If you don't know the container name find it with
docker ps

Simply run same commands as in example above
$ mkdir /var/www/html/wp-content/plugins
$ mkdir /var/www/html/wp-content/uploads
$ chown -R www-data:www-data /var/www
$ find /var/www/ -type d -exec chmod 0755 {} \;
$ find /var/www/ -type f -exec chmod 644 {} \;