[STJ-6] Migrate Fallout.Common.Tools.*Tasks API integrations

[ChrisonSimtian]

Sub-task of #83 (Newtonsoft.Json → System.Text.Json migration). Partially blocked on STJ-3.

Scope

Migrate the hand-written *Tasks.cs files in Fallout.Common.Tools.* that use Newtonsoft for external-API JSON parsing. These are integration glue with third-party services — each may use different Newtonsoft features.

Files (5)

• src/Fallout.Common/Tools/SignPath/SignPathTasks.cs — uses JObject, JToken, JValue deep access patterns
• src/Fallout.Common/Tools/Slack/SlackTasks.cs — uses utility-lib GetPropertyStringValue / GetPropertyValueOrNull (blocked on STJ-3)
• src/Fallout.Common/Tools/Twitter/TwitterTasks.cs
• src/Fallout.Common/Tools/OctoVersion/OctoVersionTasks.cs — uses AllWritableContractResolver (Newtonsoft-specific concept; need to decide on STJ equivalent or drop)
• src/Fallout.Common/Tools/Teams/Teams.Extensions.cs

Plus src/Fallout.Common/Tools/Gitter/GitterTasks.cs — verify whether still needed (Gitter discontinued in 2024).

Per-file shape varies

These talk to live external APIs (Slack messages, SignPath signing, Twitter posts, etc.). The risk profile is "did the round-trip with the external API still work?" — only catchable by manual exercise against the real API. Worth doing one task per PR rather than batching.

Acceptance

• All listed files migrated
• At least smoke-test against the live API for each (Slack post, SignPath sign request, etc.) where reasonably possible
• ./build.ps1 Test green