Update buildtools-prereqs pipelines to 1ES Pipeline templates

[lbussell]

This PR contains changes from https://github.com/dotnet/dotnet-buildtools-prereqs-docker/pull/977.

Marked as draft since I am still validating the pipelines. I do not plan to validate every pipeline as they are all so similar.

Validation runs [internal links]:

• CBL Mariner: https://dev.azure.com/dnceng/internal/_build/results?buildId=2407700&view=results
• Windows/Nano Server: https://dev.azure.com/dnceng/internal/_build/results?buildId=2408336&view=results
• All: (expected to fail in build stage) https://dev.azure.com/dnceng/internal/_build/results?buildId=2408347&view=results

Part of https://github.com/dotnet/dotnet-docker-internal/issues/4475

[lbussell]

Build failure is unrelated to changes. CI agent ran out of space. The test runs behaved as expected.

[lbussell]

Given build failure is unrelated to the change, and we've already had some successful pipeline runs in dotnet-docker-nightly, I'm merging this around PR validation.