Newbie here. Re-staking/re-delegating question

Sorry if this has been answered elsewhere, it feels like an awkward question to search for.

If I stake (X) amount in a pool through my Daedalus wallet, but then transfer an additional (Y) amount into my Daedalus wallet, do I need to take action to put that (Y) amount into the staking pool as well? Does it automatically get included on the next Epoch that its eligible for or is it sitting idle in my wallet?

The same question stands for the rewards payout, is it automatically applied to the coins working in the staking pool, or does it require additional delegation from me to get them into a pool.

Any help is appreciated.

The y amount will be added automatically to the stake amount but will became active stake in epoch x+2


Thank you!

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Same thing for the staking rewards. Automatic.