While reporting the outcome as an HTML document is not yet available in the Rust compiler, there are some crates out there which take the test runner's output in some form and convert it into structured test reports. They often depend on JSON output, which is an unstable feature at the time of writing, thus requiring a nightly toolchain. A few of these crates follow, intentionally a non-exhaustive list (do look up crates.io for more).
markdown-test-report
converts the test results into markdown, which can be easily rendered into HTML.
cargo +nightly test -- --format=json -Z unstable-options --report-time > test-report.json
markdown-test-report test-report.json test-report.md
# using pandoc for example
pandoc test-report.md -o test-report.html
junitify
turns JSON output into multiple JUnit XML reports. These too can be converted into HTML documents.
cargo +nightly test -- --format=json -Z unstable-options --report-time | junitify -o test-results/
# using xunit-viewer for example
xunit-viewer -r test-results -o test-report.html
cargo test
andcargo test -- --list
output. That appears to be what the VS Code Rust Test Explorer extension is doing as well. – Enhanced