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.lock

@@ -7,11 +7,11 @@
         ]
       },
       "locked": {
-        "lastModified": 1772587450,
-        "narHash": "sha256-yJ38xi6nRnEZIV5CEgV8xZK1dky0dVMavfFg4J7gkqw=",
+        "lastModified": 1773070962,
+        "narHash": "sha256-kHZXx+kygpVholOBsuQocCtksHo5ZWYskP64qK2Kjh0=",
         "owner": "steveyegge",
         "repo": "beads",
-        "rev": "7f41edd9c4350e5c68ebec6f9571e27833f27133",
+        "rev": "9604d30b7c746f9f04f6dea5f82996f71bb66073",
         "type": "github"
       },
       "original": {
@@ -88,11 +88,11 @@
         ]
       },
       "locked": {
-        "lastModified": 1772724442,
-        "narHash": "sha256-+H/T745sVDJAztpf3k6zz89YNrpCYsGghbO7O3O/IHw=",
+        "lastModified": 1773088127,
+        "narHash": "sha256-gJFayiBYrF0Q99AOQH29uq0Mli8KRfwReYeAh5H5evY=",
         "owner": "steveyegge",
         "repo": "gastown",
-        "rev": "112ff2c4bd145de796d20f35d35e583832a72ce1",
+        "rev": "8da798be0663af74be7960844b90038e51769203",
         "type": "github"
       },
       "original": {