I'm able to push my image to my private Docker registry but the 2nd image push is refused

Question

I am no MacOS installed Docker Desktop.

I have a private registry in Docker Hub.

I have two Dockerfiles in my project, each for one image. Both images are built successfully:

# 1st image
docker build -t myusername/my-app:1.0.3 -f Dockerfile .

# 2nd image
docker build -t myusername/my-proxy:1.0.0 -f proxy/Dockerfile .

On terminal, I firstly login with my docker id myusername:

$ docker login -u myusername docker.io
Password:
Login Succeeded

Then, I push my first image:

$ docker push myusername/my-app:1.0.3
The push refers to repository [docker.io/myusername/my-app]
e632ff00a21f: Layer already exists
...
9578c16f3f7c: Layer already exists
3141322c5cdb: Layer already exists
1.0.3: digest: sha256:43c072e10438c545697c54a76f19a41535a9fb0b7cab2a46b737c5dc497587c0 size: 2422

The push is successful!

Then I try to push my second image:

docker push myusername/my-proxy:1.0.0
The push refers to repository [docker.io/myusername/my-proxy]
c65e7e80b99d: Preparing
abcda12ed2f7: Preparing
...
1222101d19dd: Waiting
...
9e6f810a2aab: Waiting
denied: requested access to the resource is denied

However the 2nd image push to docker registry is denied. Why is that? Where could be wrong for my 2nd image push?