Core answer
Start here. This is the direct spoken answer to practice first.
Why this question matters
Deployment slots let a new App Service version start, resolve configuration, and pass checks before receiving production traffic. Their safety still depends on compatible data changes, correct sticky settings, useful warm-up, and a clear post-swap decision path.
I would use a staging deployment slot to deploy the new .NET API artifact away from production traffic. Then I would verify app settings, Key Vault references, startup, health checks, and a few smoke flows against the staging slot. After the slot is warm and looks healthy, I would swap it into production. That gives a safer release path than copying files directly over the live app.