Feature request: migrate examples and docs to .NET 10

[nicolastarzia]

Use case

.NET 10 is the current LTS release (GA Nov 2025, supported until Nov 10, 2028), while .NET 8 reaches end of support on Nov 10, 2026. The example projects and documentation in this repository still target .NET 8 — and several SAM templates were even still on the dotnet6 managed runtime while their .csproj already targeted net8.0 (a pre-existing inconsistency). New users following the examples are pointed at a runtime that is about to go out of support.

The production libraries under libraries/src/ already multi-target net8.0;net10.0, so the examples/docs are the part that lags behind.

Solution/User Experience

Migrate all example projects and documentation to .NET 10, without touching the production libraries:

• All example .csproj net8.0 → net10.0
• SAM templates Runtime dotnet6/dotnet8 → dotnet10
• aws-lambda-tools-defaults.json function-runtime → dotnet10
• Container examples: Dockerfile base images repinned to real .NET 10 digests (MCR dotnet/sdk:10.0, ECR Public lambda/dotnet:10.x, multi-arch) and publish path net6.0 → net10.0; DockerTag → dotnet10.0-v1
• Example READMEs and root README updated
• Add docs/migration-guide-v4.md

After the change, users copying an example get a project that runs on the current LTS runtime out of the box.

Alternative solutions

• Keep examples on .NET 8 until closer to its EOL — rejected, since .NET 8 EOL is imminent and the libraries already support net10.0.
• Also modernize libraries/src/ for .NET 10 / C# 14 in the same change — deferred; that is constrained by the shared net8.0+net10.0 source and LangVersion=default, and deserves its own discussion.

[powertools-for-aws-oss-automation]

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[hjgraca]

@nicolastarzia thanks for submitting the issue and pull request, Will have a look at it today.