chore: track Nx 22 AI tooling artefacts injected by generators

Nx 22 generators inject AI agent tooling into the repo via marked
sections and side files. Rather than re-deleting them after every
generator run, track the workspace-level ones and document why.

- CLAUDE.md gains a 'General Guidelines for working with Nx' section
  between Nx-managed markers; future Nx versions will update this
  section automatically without touching our project rules above.
  Pre-existing prettier-formatted blank lines added before code blocks
  are kept.
- .claude/settings.json (228 bytes) enables the nx-claude-plugins
  marketplace from nrwl/nx-ai-agents-config; tracked for contributor
  consistency. The personal .claude/settings.local.json stays
  gitignored.
- .github/ is the Nx AI skills/prompts/agents catalog. Kept despite
  being GitHub-named; it does not conflict with our Gitea workflows
  which will live under .gitea/workflows/ (per ADR-0015).
- .gitignore picks up Nx-managed transient dirs (.nx/polygraph,
  .claude/worktrees) and a trailing newline fix.

AGENTS.md is removed: it duplicated only the Nx auto-injected guidance
that CLAUDE.md already carries (CLAUDE.md is the strictly broader file
- project rules + Nx section). One source of truth for AI-agent
guidance.

.github/skills/nx-run-tasks/SKILL.md

@@ -0,0 +1,58 @@
+---
+name: nx-run-tasks
+description: Helps with running tasks in an Nx workspace. USE WHEN the user wants to execute build, test, lint, serve, or run any other tasks defined in the workspace.
+---
+
+You can run tasks with Nx in the following way.
+
+Keep in mind that you might have to prefix things with npx/pnpx/yarn if the user doesn't have nx installed globally. Look at the package.json or lockfile to determine which package manager is in use.
+
+For more details on any command, run it with `--help` (e.g. `nx run-many --help`, `nx affected --help`).
+
+## Understand which tasks can be run
+
+You can check those via `nx show project <projectname> --json`, for example `nx show project myapp --json`. It contains a `targets` section which has information about targets that can be run. You can also just look at the `package.json` scripts or `project.json` targets, but you might miss out on inferred tasks by Nx plugins.
+
+## Run a single task
+
+```
+nx run <project>:<task>
+```
+
+where `project` is the project name defined in `package.json` or `project.json` (if present).
+
+## Run multiple tasks
+
+```
+nx run-many -t build test lint typecheck
+```
+
+You can pass a `-p` flag to filter to specific projects, otherwise it runs on all projects. You can also use `--exclude` to exclude projects, and `--parallel` to control the number of parallel processes (default is 3).
+
+Examples:
+
+- `nx run-many -t test -p proj1 proj2` — test specific projects
+- `nx run-many -t test --projects=*-app --exclude=excluded-app` — test projects matching a pattern
+- `nx run-many -t test --projects=tag:api-*` — test projects by tag
+
+## Run tasks for affected projects
+
+Use `nx affected` to only run tasks on projects that have been changed and projects that depend on changed projects. This is especially useful in CI and for large workspaces.
+
+```
+nx affected -t build test lint
+```
+
+By default it compares against the base branch. You can customize this:
+
+- `nx affected -t test --base=main --head=HEAD` — compare against a specific base and head
+- `nx affected -t test --files=libs/mylib/src/index.ts` — specify changed files directly
+
+## Useful flags
+
+These flags work with `run`, `run-many`, and `affected`:
+
+- `--skipNxCache` — rerun tasks even when results are cached
+- `--verbose` — print additional information such as stack traces
+- `--nxBail` — stop execution after the first failed task
+- `--configuration=<name>` — use a specific configuration (e.g. `production`)