How is it possible to set a directory permission, so the group can both read and write files in it? (Regardless who created a file)

I created a directory, which is owned by the www-data group. I would like to make the files in it writeable by the members of the group, no matter who created the file. My username is pi. I tried it like this:

mkdir ./shared
sudo chown pi ./shared
sudo chgrp www-data ./shared
sudo chmod -R 770 ./shared
sudo chmod g+sw ./shared

If I check it with ls -l, it looks like this:

drwxrws--- 2 pi   www-data 4096 sept 28 17:10  shared

I created a new file in it:

cd ./shared
touch ./test.txt

But if I check, the group has no write right for the new test.txt

-rw-r--r-- 1 pi www-data 0 sept 28 17:10 test.txt

What do I wrong? I can not run sudo chmod -R 770 ./shared each time, a new file is created in the directory by a script/webserver. How is it possible to create a shared directory, where both the owner and the group members have read and write rights for the files, regardless who created a specific file?