aws-lambda-dotnet:7 image with sdk preinstalled?

I am trying to understand how one is supposed compile+test a dotnet 7 project (no ASP).

According to documentation:

• https://docs.aws.amazon.com/lambda/latest/dg/csharp-image.html

I can only find dotnet runtime pre-installed:

FROM public.ecr.aws/lambda/dotnet:7

Looking at the typical template in gitlab:

• https://gitlab.com/gitlab-org/project-templates/dotnetcore#whats-contained-in-this-project

a reference image with sdk pre-installed is used:

image: microsoft/dotnet:latest

Which image should one use to build/test/deploy code that is suppose to run on public.ecr.aws/lambda/dotnet:7 ? Here is what I see on my side:

> docker run -it --entrypoint /var/lang/bin/dotnet public.ecr.aws/lambda/dotnet:7 --info

Host:
  Version:      7.0.7
  Architecture: x64
  Commit:       5b20af47d9

.NET SDKs installed:
  No SDKs were found.

.NET runtimes installed:
  Microsoft.AspNetCore.App 7.0.7 [/var/lang/bin/shared/Microsoft.AspNetCore.App]
  Microsoft.NETCore.App 7.0.7 [/var/lang/bin/shared/Microsoft.NETCore.App]

Other architectures found:
  None

Environment variables:
  DOTNET_ROOT       [/var/lang/bin]

global.json file:
  Not found

Learn more:
  https://aka.ms/dotnet/info

Download .NET:
  https://aka.ms/dotnet/download

Obviously I could use mcr.microsoft.com/dotnet/sdk:7.0 as base image for compilation, do the publish step, store as artefact, then load public.ecr.aws/lambda/dotnet:7 load artefacts from previous step and then eventually do the testing...but that seems overly complex to setup.

Simple solution is to build it during a pre-build stage of gitlab-ci:

stages:
  - image
  - build
  - test
  - deploy

Prepare docker image:
  stage: image
  image: docker:stable
  tags:
    - dind
    - linux
  only:
    changes:
      - docker/Dockerfile
  script:
    - docker login -u $CI_REGISTRY_USER -p $CI_JOB_TOKEN $CI_REGISTRY
    - docker pull $CI_REGISTRY_IMAGE:latest || true
    - docker build --build-arg BUILDKIT_INLINE_CACHE=1
      --cache-from $CI_REGISTRY_IMAGE:latest
      --tag $CI_REGISTRY_IMAGE:$CI_COMMIT_SHA docker
    - docker tag $CI_REGISTRY_IMAGE:$CI_COMMIT_SHA $CI_REGISTRY_IMAGE:latest
    - docker push $CI_REGISTRY_IMAGE:latest

where Dockerfile is simply:

FROM amazonlinux:2

ARG SDK_VERSION=6.0
ENV SDK_VERSION=$SDK_VERSION

RUN rpm -Uvh https://packages.microsoft.com/config/centos/7/packages-microsoft-prod.rpm
RUN yum install -y dotnet-sdk-$SDK_VERSION