Convert all `LiveTests` to `Recorded` tests

[scbedd]

Issues are filed parented to this issue. Instructions within each.

Keyvault has been completed prior to this issue population:

• tools/Azure.Mcp.Tools.KeyVault/tests/Azure.Mcp.Tools.KeyVault.LiveTests/Azure.Mcp.Tools.KeyVault.LiveTests.csproj
  • Migrate Keyvault tool to recorded tests #1080