From the Super Mario Wiki
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During the events of Front-Door Key, Luigi is sent to the gate near the mansion. Here, the player can see the ravine and cliff the mansion is by. The player has to cross a few sets of rafters, but they break once Luigi gets near the entrance.
When Luigi gets near the entrance, he tries to use the key to open the main door, but the Polterpup steals it before Luigi gets a chance to open it, making Luigi chase it down the well near here. Luigi can look through the windows here or shine the gargoyles.
During Double Trouble, the Veranda is where Luigi must use the key to open the door to get in. Luigi can no longer go back to the gate or the basement of the mansion due to the rafters being broken, and the well's red ball is down.
The Veranda is irrelevant for the rest of the missions until Terrifying Invasion, where the player can now revisit the well, but they still cannot go back to the gate.