Notice from the output of docker ps that the postgres container has exited, i.e. it is not running. This is why you cannot exec into it.
When you first ran it, it should have told you
Error: Database is uninitialized and superuser password is not specified.
You must specify POSTGRES_PASSWORD to a non-empty value for the
superuser. For example, "-e POSTGRES_PASSWORD=password" on "docker run".
You may also use "POSTGRES_HOST_AUTH_METHOD=trust" to allow all
connections without a password. This is *not* recommended.
See PostgreSQL documentation about "trust":
https://www.postgresql.org/docs/current/auth-trust.html
which tells you how to run it properly.
For example
docker run -e POSTGRES_PASSWORD=MyReallySecurePassword postgres
lots of output followed by…
2023-10-29 13:20:47.061 UTC [1] LOG: database system is ready to accept connections
$ docker ps
CONTAINER ID IMAGE COMMAND CREATED STATUS PORTS NAMES
fbc49cf88ec3 postgres "docker-entrypoint.s…" 2 minutes ago Up About a minute 5432/tcp nostalgic_sutherland
$