Does removing some coins from a staked wallet unstake the remaining amount?

Let’s say I have a wallet with 100 Ada that I have staked to a pool. As time goes by I will earn staking rewards which as I understand it will automatically be added to the wallet and staked to that same pool as well. Let’s say after some time passes I now have 120 Ada in that wallet 100 original plus the 20 I received from rewards. Let’s say I now want to spend or transfer 30 Ada from the wallet. At that point does the remaining 90 Ada get unstaked and force me to restake it? Or does it stay staked with its current pool and I don’t have to worry about it?

In a similar vein if I had a wallet with 100 Ada staked and someone sent me some additional Ada to that wallet would it automatically get staked with the existing coins?

I bring this up as I’m trying to organize my funds into wallets that hopefully require minimal maintenance.

If there is a FAQ or video on how this works somewhere please let me know.