Update flake inputs, deduplicate beads/gastown package definitions

- Update beads and gastown flake inputs and vendorHashes
- Remove merged-upstream patches for gastown and beads
- Deduplicate beads/gastown build definitions in home role by using
  callPackage to reference shared packages/ definitions
- Pin dolt to v1.82.4 (gastown requires >= 1.82.4)

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

flake.nix

@@ -113,6 +113,19 @@
       (ufinal: uprev: {
         claude-code = uprev.callPackage ./packages/claude-code {};
       })
+      # Pin dolt to v1.82.4 (gastown requires >= 1.82.4)
+      (ufinal: uprev: {
+        dolt = uprev.dolt.overrideAttrs (old: rec {
+          version = "1.82.4";
+          src = uprev.fetchFromGitHub {
+            owner = "dolthub";
+            repo = "dolt";
+            tag = "v${version}";
+            hash = "sha256-mavL3y+Kv25hzFlDFXk7W/jeKVKlCBjlc67GkL3Jcwk=";
+          };
+          vendorHash = "sha256-K1KzsqptZxO5OraWKIXeqKuVSzb6E/Mjy3c5PQ7Rs9k=";
+        });
+      })
     ];
 
     nixosModules = [