Direct answer
If your APY drops below competitive alternatives, quantify the annual dollar gap, check whether the destination account has gotchas, then move only idle cash in stages.
Why this is not generic
Current rate endpoint
Dollar-gap calculator
Switch workflow
Do not react to one basis point
Small moves may not justify switching. Calculate the dollar gap on your actual balance before making the move.
Check account conditions
A higher APY can have direct deposit, balance tier, or membership requirements. Read the destination account terms before funding.
Use a staged move
A rate drop is a reason to compare, not a reason to break bill pay. Keep operating cash stable while moving idle savings.