The error budget is what the objective is for

An objective of 99.5% is also a statement that 0.5% of requests may fail, and that allowance is a resource with a use.

99.5% over 30 days = 3h 36m of budget

spent  47m   an incident on the 4th
       12m   a bad deploy on the 11th
       ---
       59m   remaining: 2h 37m

and the decision it enables:
  budget healthy  → ship. take risks. deploy on Friday.
  budget spent    → stop feature work. fix reliability.

that rule has to be agreed BEFORE it is needed.

The budget turns reliability from an argument into arithmetic, which is the whole point — “is it safe to ship this” has an answer that is not a matter of temperament. The rule about what happens when it is exhausted is the part that requires somebody with authority to agree it, and without that the budget is a number on a dashboard. An objective nobody would ever act on is set too low and should be lowered further until it constrains something.