回答編集履歴
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追記
test
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@@ -1,17 +1,32 @@
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[Shapely](https://shapely.readthedocs.io/en/stable/index.html)の[unary_union](https://shapely.readthedocs.io/en/stable/reference/shapely.unary_union.html#shapely-unary-union)が使えそうです。
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結合後、直線区間中に連続する点は残りますが、それを除く方法はおそらく難しくなく、Shapelyの関数としても用意されているかもしれません。
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### 追記
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不要な点の削除は[normalize](https://shapely.readthedocs.io/en/stable/reference/shapely.Polygon.html#shapely.Polygon.normalize)して[simplify](https://shapely.readthedocs.io/en/stable/reference/shapely.Polygon.html#shapely.Polygon.simplify)すればよい感じです。
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参考：[Simplify method can not simplify duplicated vertices of a ring #1638](https://github.com/shapely/shapely/issues/1638)
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```Python
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import matplotlib.pyplot as plt
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import shapely
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from shapely.geometry import Polygon
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# ポリゴンは反時計回りで定義
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p1 = Polygon([(10,0),(10,10),(20,10),(20,15),(25,15),(25,5),(30,5),(30,0)][::-1])
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p2 = Polygon([(5,25),(25,25),(25,15),(20,15),(20,10),(15,10),(15,20),(5,20)][::-1])
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p3 = shapely.unary_union([p1,p2])
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p
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plt.plot(*p3.exterior.xy, marker="o")
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plt.show()
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print(p3)
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# POLYGON ((25 15, 25 5, 30 5, 30 0, 10 0, 10 10, 15 10, 15 20, 5 20, 5 25, 25 25, 25 15))
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# 不要な点を取り除く
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p3 = p3.normalize().simplify(0.1)
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plt.plot(*p3.exterior.xy, marker="o")
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plt.show()
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print(p3)
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# POLYGON ((5 20, 5 25, 25 25, 25 5, 30 5, 30 0, 10 0, 10 10, 15 10, 15 20, 5 20))
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# 重ならない
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p1 = Polygon([(0,0),(1,0),(1,1),(0,1),(0,0)])
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print(shapely.unary_union([p1,p2]))
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# POLYGON ((3 1, 3 0, 0 0, 0 1, 0 3, 3 3, 3 1), (1 1, 2 1, 2 2, 1 2, 1 1))
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```
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追記
test
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@@ -11,5 +11,42 @@
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p3 = shapely.unary_union([p1,p2])
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print(p3)
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# POLYGON ((25 15, 25 5, 30 5, 30 0, 10 0, 10 10, 15 10, 15 20, 5 20, 5 25, 25 25, 25 15))
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# 重ならない
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p1 = Polygon([(0,0),(1,0),(1,1),(0,1),(0,0)])
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p2 = Polygon([(2,0),(3,0),(3,1),(2,1),(2,0)])
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print(shapely.unary_union([p1,p2]))
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# MULTIPOLYGON (((0 0, 1 0, 1 1, 0 1, 0 0)), ((2 0, 3 0, 3 1, 2 1, 2 0)))
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# 内包
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p1 = Polygon([(0,0),(3,0),(3,3),(0,3),(0,0)])
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p2 = Polygon([(1,1),(2,1),(2,2),(1,2),(1,1)])
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print(shapely.unary_union([p1,p2]))
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# POLYGON ((0 0, 0 3, 3 3, 3 0, 0 0))
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# 辺で接する
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p1 = Polygon([(0,0),(1,0),(1,1),(0,1),(0,0)])
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p2 = Polygon([(1,0),(2,0),(2,1),(1,1),(1,0)])
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print(shapely.unary_union([p1,p2]))
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# POLYGON ((1 0, 0 0, 0 1, 1 1, 2 1, 2 0, 1 0))
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# 点で接する
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p1 = Polygon([(0,0),(1,0),(1,1),(0,1),(0,0)])
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p2 = Polygon([(1,1),(2,1),(2,2),(1,2),(1,1)])
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print(shapely.unary_union([p1,p2]))
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# MULTIPOLYGON (((1 1, 1 0, 0 0, 0 1, 1 1)), ((1 1, 1 2, 2 2, 2 1, 1 1)))
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# 重複
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p1 = Polygon([(0,0),(2,0),(2,2),(0,2),(0,0)])
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p2 = Polygon([(0,1),(2,1),(2,3),(0,1)])
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print(shapely.unary_union([p1,p2]))
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# POLYGON ((2 1, 2 0, 0 0, 0 1, 0 2, 1 2, 2 3, 2 2, 2 1))
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# 穴ができる
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p1 = Polygon([(0,0),(3,0),(3,1),(0,1),(0,0)])
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p2 = Polygon([(2,1),(3,1),(3,3),(0,3),(0,1),(1,1),(1,2),(2,2),(2,1)])
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print(shapely.unary_union([p1,p2]))
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# POLYGON ((3 1, 3 0, 0 0, 0 1, 0 3, 3 3, 3 1), (1 1, 2 1, 2 2, 1 2, 1 1))
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```
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