Opening the book…
The gap between a mistake happening and someone owning it is where a team's trust quietly drains. If you claim it first, the conversation moves to the fix within a minute; if you wait, everyone spends the morning working out who is exposed. Owning it early also costs you less, because it reads as confidence rather than confession.
When you realise you got it wrong, say so in the same channel where the work happened, plainly and without a paragraph of context. One sentence of ownership, one sentence on what you are doing about it. Do not soften it with "we" when it was you, and do not perform contrition — the point is to clear the air, not to be absolved.
When the failure is genuinely shared, claiming all of it is its own kind of vanity and it robs others of the chance to learn. And if the mistake is being investigated formally or has legal weight, get advice on the wording before you publish anything.