feat(parse): add parse_duration_to_days for duration string conversion

Problem: The archive command accepted only a bare integer for days,
inconsistent with the `+Nd`/`+Nw`/`+Nm` duration syntax used elsewhere.

Solution: Add `parse_duration_to_days()` supporting `Nd`, `Nw`, `Nm`,
and bare integers. Returns nil on invalid input for caller error handling.

spec/parse_spec.lua

@@ -416,6 +416,48 @@ describe('parse', function()
     end)
   end)
 
+  describe('parse_duration_to_days', function()
+    it('parses days suffix', function()
+      assert.are.equal(7, parse.parse_duration_to_days('7d'))
+    end)
+
+    it('parses weeks suffix', function()
+      assert.are.equal(21, parse.parse_duration_to_days('3w'))
+    end)
+
+    it('parses months suffix (approximated as 30 days)', function()
+      assert.are.equal(60, parse.parse_duration_to_days('2m'))
+    end)
+
+    it('parses bare integer as days', function()
+      assert.are.equal(30, parse.parse_duration_to_days('30'))
+    end)
+
+    it('returns nil for nil input', function()
+      assert.is_nil(parse.parse_duration_to_days(nil))
+    end)
+
+    it('returns nil for empty string', function()
+      assert.is_nil(parse.parse_duration_to_days(''))
+    end)
+
+    it('returns nil for unrecognized input', function()
+      assert.is_nil(parse.parse_duration_to_days('xyz'))
+    end)
+
+    it('returns nil for negative numbers', function()
+      assert.is_nil(parse.parse_duration_to_days('-7d'))
+    end)
+
+    it('handles single digit', function()
+      assert.are.equal(1, parse.parse_duration_to_days('1d'))
+    end)
+
+    it('handles large numbers', function()
+      assert.are.equal(365, parse.parse_duration_to_days('365d'))
+    end)
+  end)
+
   describe('input_date_formats', function()
     before_each(function()
       config.reset()