Network: Fail to set DNS server and search domain on Debian12

# Bug report
Fail to set DNS server and search domain on Debian12

## Steps to reproduce the problem
This issue happens on both DHCP and STATIC IP customization on Debian 12 when using cloud-init as engine.

With DHCP IP and DNS settings, the same issue was reported on Ubuntu 18.04 at https://bugs.launchpad.net/ubuntu/+source/cloud-init/+bug/1776452, later Ubuntu moved to Netplan which doesn't have this issue any more. But for Debian, it's still using eni as networking configuration, so this issue still reproduces on Debian.

With STATIC IP and DNS settings, cloud-init sets DNS server and search domain in /etc/network/interface.d/50-cloud-init file which doesn't take effect.

## Environment details
- Cloud-init version: 22.4.2
- Operating System Distribution: Debian 12.0
- Cloud provider, platform or installer type: VMware vSphere

## cloud-init logs
[cloud-init.tar.gz](https://github.com/canonical/cloud-init/files/12067064/cloud-init.tar.gz)

Tracked by VMware internal bug 3234146

Start with the attached cloud-init logs and the Debian ENI networking path that generates /etc/network/interface.d/50-cloud-init. Reproduce the DHCP and static-IP cases on Debian 12, then verify how DNS servers and the search domain are applied. Done means both configurations set effective DNS and search-domain values rather than only writing them to an ineffective file.

Written by the indexing model from the issue text.