Unable to connect worker node to master using K3S

I am trying to setup a K3S cluster for learning purposes but I am having trouble connecting the master node with agents. I have looked several tutorials and discussions on this but I can't find a solution. I know I am probably missing something obvious (due to my lack of knowledge), but still help would be much appreciated.

I am using two AWS t2.micro instances with default configuration.

When ssh into the master and installed K3S using

curl -sfL https://get.k3s.io | sh -s - --no-deploy traefik --write-kubeconfig-mode 644 --node-name k3s-master-01

with kubectl get nodes, I am able to see the master

NAME            STATUS   ROLES                  AGE   VERSION
k3s-master-01   Ready    control-plane,master   13s   v1.23.6+k3s1

So far it seems I am doing things right. From what I understand, I am supposed to configure the kubeconfig file. So, I accessed it by using

cat /etc/rancher/k3s/k3s.yaml

I copied the configuration file and the server info to match the private IP I took from AWS console, resulting in something like this

apiVersion: v1
clusters:
- cluster:
    certificate-authority-data: <lots_of_info>
    server: https://<master_private_IP>:6443
  name: default
contexts:
- context:
    cluster: default
    user: default
  name: default
current-context: default
kind: Config
preferences: {}
users:
- name: default
  user:
    client-certificate-data: <my_certificate_data>
    client-key-data: <my_key_data>

Then, I ran vi ~/.kube/config, and there I pasted the kubeconfig file

Finally, I grabbed the token with cat /var/lib/rancher/k3s/server/node-token, ssh into the other machine and then run the following

curl -sfL https://get.k3s.io | K3S_NODE_NAME=k3s-worker-01 K3S_URL=https://<master_private_IP>:6443 K3S_TOKEN=<master_token> sh -

The output is

[INFO]  Finding release for channel stable
[INFO]  Using v1.23.6+k3s1 as release
[INFO]  Downloading hash https://github.com/k3s-io/k3s/releases/download/v1.23.6+k3s1/sha256sum-amd64.txt
[INFO]  Downloading binary https://github.com/k3s-io/k3s/releases/download/v1.23.6+k3s1/k3s
[INFO]  Verifying binary download
[INFO]  Installing k3s to /usr/local/bin/k3s
[INFO]  Skipping installation of SELinux RPM
[INFO]  Creating /usr/local/bin/kubectl symlink to k3s
[INFO]  Creating /usr/local/bin/crictl symlink to k3s
[INFO]  Creating /usr/local/bin/ctr symlink to k3s
[INFO]  Creating killall script /usr/local/bin/k3s-killall.sh
[INFO]  Creating uninstall script /usr/local/bin/k3s-agent-uninstall.sh
[INFO]  env: Creating environment file /etc/systemd/system/k3s-agent.service.env
[INFO]  systemd: Creating service file /etc/systemd/system/k3s-agent.service
[INFO]  systemd: Enabling k3s-agent unit
Created symlink /etc/systemd/system/multi-user.target.wants/k3s-agent.service → /etc/systemd/system/k3s-agent.service.
[INFO]  systemd: Starting k3s-agent

By this output, it looks like I have created an agent. However, when I run kubectl get nodes in the master, I still get

NAME            STATUS   ROLES                  AGE   VERSION
k3s-master-01   Ready    control-plane,master   12m   v1.23.6+k3s1

What is the thing I was supposed to do in order to get the agent connected to the master? I am guess I am probably missing something simple, but I just can't seem to find the solution. I've read all the documentation but it is still not clear to me where I am making the mistake. I've tried saving the private master IP and token into the agent as environmental variables with export K3S_TOKEN=master_token and K3S_URL=master_private_IP and then simply running curl -sfL https://get.k3s.io | sh - but I still can't see the worker nodes when running kubectl get nodes

Any help would be appreciated.