How can I implement a system in my poker game that allows players to sit at a new table and automatically open a new window for gameplay without requiring the game engine to reload, while still managing the necessary asset loading in the background?
You need to clarify a lot here. What do you mean by “table” and “window”? What does it mean to “sit at a table”? Do you have a 3d environment with actual tables? Or was that just a metaphor for a “game session”? We can’t tell what kind of game you have in mind. The game design is on your side. Also Unity can be used on various platforms and the possibilities you have in each can be quite different when it comes to interactions with things outside the game itself (for example when the game is embedded in a website). You need to add much more details to describe your current situation and idea before we can even attempt to guide you in a direction. We don’t really like guessing games when it comes to question asked here 
Questions should be precise and detailed. So feel free to edit your question and add more information.
I’d spawn each table view as its own additive scene and keep a lightweight manager scene loaded so you don’t reload the engine every time. Async scene loading works well for pulling in assets quietly in the background. Kind of like how I switch between tabs on sites like casinos not on Gamestop without the whole page kicking me back to the start. This setup keeps things smooth while you juggle multiple tables.
You can continue the game and just open a new game screen while loading table assets in the background.
Many games do this to save reloading and time.
Learning it the right way is better than using shortcuts like Lucky Patcher.