People shouldn't be gossiping about this, as disciplinary matters are confidential and should only be divulged on a need to know basis.
I work in HR and you highlighting your error shows honesty and integrity. I don't know how serious it was, but if I was advising a manager on what action to take and you hadn't done something similar in the past, then I would suggest non disciplinary action.
You said it happened last week and you already have a warning...that's quick. Was an investigation carried out? I know you pointed out the error, but in my organisation we would still do an investigation.
You don't have to say on the thread, but Im wondering if it's something that could be gross misconduct....if it is, then I would say they've gone easy on you, which is likely to be as a result of your honesty.
If you feel training was a factor, then you need to raise this with your manager and try and get support.
Companies generally only give details of job title and dates of employment these days due to GDPR
It depends on the organisation policy. We can provide factual information for references, which discloses number of days sickness absence and disciplinaries in the last 2 years.