How do I obtain the debian-installer for Ubuntu Server 18.04.3 LTS?

Ubuntu Server ISO images with debian-installer continue to be available, including for 18.04.3 LTS. There is no need to use media for an earlier point release. You most likely want ubuntu-18.04.3-server-amd64.iso, though other architectures are available.

On the main download page, the Use the traditional installer link takes you to a section for the "Alternative Ubuntu Server installer." These are the non-live ISO images for Ubuntu Server that use debian-installer (as Ubuntu Server has used exclusively for most of its history). This is in contrast to the more recently introduced live server images, which use curtin.

The link there for 18.04.3 LTS takes you to http://cdimage.ubuntu.com/releases/18.04.3/release/. The alternative server ISOs have names like ubuntu-18.04.3-server-arm64.iso; this indicates they use debian-installer. This is in contrast to the server ISOs offered at http://releases.ubuntu.com/18.04.3/, which have names like ubuntu-18.04.3-live-server-amd64.iso and use curtin.

http://cdimage.ubuntu.com/releases/18.04.3/release/ has other architectures, .torrent and .jigdo files (including for the alternative server ISO), the preinstalled images, and manifest and checksum files for everything offered there.