ESRP recently added support for publishing Rust packages to https://crates.io. This support is in v10 of the EsrpRelease task (EsrpRelease@10), but MicroBuild.Publish is still using v9. I recently asked the MicroBuild.Publish folks when they would upgrade, but haven't heard back yet. You can check which version of EsrpRelease is currently in use by looking for that task's output in any release pipeline run that uses it. For example, here's what I found in a recent run from sarif-tools:

Once MicroBuild.Publish upgrades to EsrpRelease@10, we should create a pipeline (similar to https://github.com/microsoft/lsprotocol/blob/main/azure-pipelines/release-pypi.yml) to publish the Rust package. They could also be combined into one pipeline, but my impression is that we don't always want/need to ship both at any given time.