Stop using Microsoft/GitHub's `ubuntu-*` images as the linux-x64 build image for .NET pipelines

Today, we use the following default images for linux-amd64 builds:
- Public: `ubuntu-latest`
- Internal: `1es-ubuntu-2204`

Downsides of using these images:
- We (.NET) do not control the contents of these images. And they contain _a lot_ of [stuff](https://github.com/actions/runner-images/blob/ubuntu22/20250602.1/images/ubuntu/Ubuntu2204-Readme.md).
- Using them causes slower builds in two ways
- Cleaning off the pre-loaded docker images takes extra time
- Public PR validation using the default pool ("Azure Pipelines") and the Microsoft-hosted images is limited to 200 concurrent jobs across the entire dotnet org. Oftentimes we have to wait for agents during PR validation. We have much more capacity in other pools like `NetCore-Public`. Available pools can be found at https://dev.azure.com/dnceng-public/public/_settings/agentqueues

To me it looks like we should use the following images, until Azure Linux 3 images are available from dnceng:
- Public: `build.ubuntu.2204.amd64.open`
- Internal: `build.ubuntu.2204.amd64`

See the following code:

https://github.com/dotnet/docker-tools/blob/99554581b18e4818ca393d430a32f242007ea0fa/eng/common/templates/variables/dotnet/common.yml#L21-L22

https://github.com/dotnet/docker-tools/blob/99554581b18e4818ca393d430a32f242007ea0fa/eng/common/templates/variables/common.yml#L68-L69

https://github.com/dotnet/docker-tools/blob/99554581b18e4818ca393d430a32f242007ea0fa/eng/common/templates/stages/dotnet/publish.yml#L48-L56

https://github.com/dotnet/docker-tools/blob/99554581b18e4818ca393d430a32f242007ea0fa/eng/common/templates/stages/dotnet/build-and-test.yml#L57-L66