This page of the Genshin Impact game guide explains what the House System is, what Serenitea pot is for, how to get it and what is required to obtain this item.
The House System is a new feature in the game, which allows you to go to the world where your new house will be located, ready for upgrading. The Serenitea Pot is quite an interesting object tied to one quest. It will allow you to move into your home, giving you the option to "work" on it, decorate it and craft new decorative items.
How to obtain the Serenitea Pot?
The Serenitea Pot is an item that you can only unlock by completing the quest series Archon Quest, Chapter I, Act III: A New Star Approaches. The quest is called A Teapot to Call Home. You also need at least Adventure Rank 35 to unlock this quest.
Once you have access to the quest, head to Liyue city. There, the quest will lead you to Madame Ping, where you will begin the quest. In general, completing this quest will consist of going to various NPCs in the city, no fights are involved.
When you complete the quest, you will receive the Serenitea Pot from Madame Ping, which will be in your equipment, in the Gadget tab. You can equip it and then use it to move to a new area where your new home will be located.
What is the Serenitea Pot for?
The Serenitea Pot is actually used to move your character to a new location, where your new home can be found. You will be able to upgrade it, decorate it, expand your collection of decorations and buildings at your discretion.
When you use the Serenitea Pot for the first time, you will have to choose one of the three possible layouts. Keep in mind that you won't be initially able to switch to another layout, as this is a reward for improving the Trust Rank level. Thus, you should think carefully before choosing your preferred layout.
Tubby - what is she for?
Tubby is a ghost NPC who will tell you more about this place. However, her role is not limited to collecting information about the new world you appeared in. You can increase your Trust Rank with her. For each level of Trust Rank, you will get additional rewards. Trust Rank can be increased by crafting furniture items, that is, decorations.
Additionally, you will be able to change the layout of your new house (only when you unlock the appropriate level of TR), buy various decorations that you can then use, and even craft them if you have the blueprints and materials needed to complete the project.
You will receive diagrams every time you complete one of the tasks in the Adeptal Mirror tab. Once you have one, activate it in your equipment, talk to the ghost and then go to the Creation tab. There you will see your current blueprints and the necessary objects to create a particular project.