I created the template from scratch and after some reading I found that it's important to remove any previous netplan configurations. So the template has an empty /etc/netplan directory.

I added the following to my "Network config" box when creating the VM:

version: 2
renderer: networkd
ethernets:
  eth0:
    addresses:
      - 172.27.19.65/24
    gateway4: 172.27.19.1
    nameservers:
      addresses:
        - 192.168.1.15
        - 192.168.2.15

And after the first boot of the template I can see that the following is indeed created in /etc/netplan/50-cloud-init.yaml:

network:
    ethernets:
        eth0:
            addresses:
            - 172.27.19.65/24
            gateway4: 172.27.19.1
            nameservers:
                addresses:
                - 192.168.1.15
                - 192.168.2.15
    renderer: networkd
    version: 2

But the network is never brought up. In the cloud-init log I see the following:

2021-04-02 01:12:09,262 - stages.py[DEBUG]: applying net config names for {'version': 2, 'renderer': 'networkd', 'ethernets': {'eth0': {'addresses': ['172.27.19.65/24'], 'gateway4': '172.27.19.1', 'nameservers': {'addresses': ['192.168.1.15', '192.168.2.15']}}}}
2021-04-02 01:12:09,263 - __init__.py[DEBUG]: no interfaces to rename
2021-04-02 01:12:09,263 - stages.py[INFO]: Applying network configuration from ds bringup=False: {'version': 2, 'renderer': 'networkd', 'ethernets': {'eth0': {'addresses': ['172.27.19.65/24'], 'gateway4': '172.27.19.1', 'nameservers': {'addresses': ['192.168.1.15', '192.168.2.15']}}}}
2021-04-02 01:12:09,265 - __init__.py[DEBUG]: Selected renderer 'netplan' from priority list: None
2021-04-02 01:12:09,265 - network_state.py[DEBUG]: NetworkState Version2: missing "macaddress" info in config entry: eth0: {'addresses': ['172.27.19.65/24'], 'gateway4': '172.27.19.1', 'nameservers': {'addresses': ['192.168.1.15', '192.168.2.15']}}
2021-04-02 01:12:09,265 - network_state.py[DEBUG]: v2(ethernets) -> v1(physical):
{'type': 'physical', 'name': 'eth0', 'mac_address': None, 'subnets': [{'type': 'static', 'address': '172.27.19.65/24', 'gateway': '172.27.19.1', 'dns_nameservers': ['192.168.1.15', '192.168.2.15']}]}
2021-04-02 01:12:09,268 - network_state.py[DEBUG]: v2_common: handling config:
{'eth0': {'addresses': ['172.27.19.65/24'], 'gateway4': '172.27.19.1', 'nameservers': {'addresses': ['192.168.1.15', '192.168.2.15']}}}
2021-04-02 01:12:09,269 - netplan.py[DEBUG]: V2 to V2 passthrough
2021-04-02 01:12:09,270 - util.py[DEBUG]: Writing to /etc/netplan/50-cloud-init.yaml - wb: [644] 649 bytes
2021-04-02 01:12:09,282 - subp.py[DEBUG]: Running command ['netplan', 'generate'] with allowed return codes [0] (shell=False, capture=True)
2021-04-02 01:12:09,455 - subp.py[DEBUG]: Running command ['udevadm', 'test-builtin', 'net_setup_link', '/sys/class/net/eth0'] with allowed return codes [0] (shell=False, capture=True)
2021-04-02 01:12:09,460 - subp.py[DEBUG]: Running command ['udevadm', 'test-builtin', 'net_setup_link', '/sys/class/net/lo'] with allowed return codes [0] (shell=False, capture=True)
2021-04-02 01:12:09,463 - main.py[DEBUG]: [local] Exiting. datasource DataSourceNoCloud [seed=/dev/xvdb][dsmode=net] not in local mode.

You can see that it runs netplan generate but never netplan apply. From the logs it looks like the problem might be that the datasource isn't in "local" mode. But I thought I took care of that because I have the following in my /etc/cloud/cloud.cfg:

datasource_list: [ NoCloud, None ]
datasource:
  NoCloud:
    dsmode: local

I'm also wondering if there's an issue related to the line in the logs NetworkState Version2: missing "macaddress" info in config entry: eth0:.

In any case I've been banging my head against the wall with this for too long... So I'd appreciate any guidance.