GH-47058: [Release] Update Release Management Guide to reflect status in preparation for Arrow 22 (#47474)

### Rationale for this change

The Release suffered some changes around automated signature and verification tasks that were not reflected on the Release Management guide.

The C# implementation has also been moved to it own repository, I took the time to reflect that change on the Release Management guide too.

### What changes are included in this PR?

Update release management guide to cover automated signing of source artifact and automated trigger for verification tasks.
Remove C# from the Release management guide and post-steps.

### Are these changes tested?

Not necessary but I'll trigger preview docs.

### Are there any user-facing changes?

No

* GitHub Issue: #47058

Authored-by: Raúl Cumplido <[email protected]>
Signed-off-by: Raúl Cumplido <[email protected]>

Author: raulcd

.pre-commit-config.yaml

@@ -361,8 +361,8 @@ repos:
           ?^dev/release/07-binary-verify\.sh$|
           ?^dev/release/binary-recover\.sh$|
           ?^dev/release/post-03-binary\.sh$|
-          ?^dev/release/post-10-docs\.sh$|
-          ?^dev/release/post-11-python\.sh$|
+          ?^dev/release/post-08-docs\.sh$|
+          ?^dev/release/post-09-python\.sh$|
           ?^dev/release/setup-rhel-rebuilds\.sh$|
           ?^dev/release/utils-generate-checksum\.sh$|
           ?^python/asv-install\.sh$|
@@ -387,8 +387,8 @@ repos:
           ?^dev/release/05-binary-upload\.sh$|
           ?^dev/release/binary-recover\.sh$|
           ?^dev/release/post-03-binary\.sh$|
-          ?^dev/release/post-10-docs\.sh$|
-          ?^dev/release/post-11-python\.sh$|
+          ?^dev/release/post-08-docs\.sh$|
+          ?^dev/release/post-09-python\.sh$|
           )
   - repo: https://github.com/trim21/pre-commit-mirror-meson
     rev: v1.6.1

dev/release/post-07-csharp.sh

@@ -75,12 +75,12 @@ def bump_versions(*targets)
     case bump_type
     when :minor, :patch
       sh(env,
-         "dev/release/post-11-bump-versions.sh",
+         "dev/release/post-10-bump-versions.sh",
          released_version,
          @release_version)
     else
       sh(env,
-         "dev/release/post-11-bump-versions.sh",
+         "dev/release/post-10-bump-versions.sh",
          released_version,
          @next_version)
     end