Why do some projects like to have their liquidity staked?

Help me understand this.

I provide liquidity for project X with an ETH pairing at 50:50 X/ETH on Uniswap. In return I receive LP-Tokens for 50:50 X/ETH that represent the value of my liquidity + fees earned. I will need these LP-Tokens to pull out my liquidity + fees earned at any given time and move on.

Now, project X has a partner program called project XY ( they work together within the same ecosystem). Project XY offers me to earn XY Tokens if I were to "stake" my LP-Tokens from project X with them.

Here are my questions:

How and Why does Staking work with LP-Tokens? ( in nuanced detail would be great )

Why would Project XY like to have Project X's LP-Tokens staked with them? ( other than obvious things such as stability of liquidity, please mention every detail if you know the answer to this )

Are there different kinds of Staking in regard to ERC20 tokens and if so, how does one research relevant differences and what are they?

As I'm still learning, I might not be able to ask all the important questions in this regard., so if I have left an obvious relevant question to this topic out, feel free to put it in the room and answer it too if you know how.

Thanks in advance for anyone sharing his knowledge on this.