I understand your reluctantance to email HR as you want to keep your head down for a few years. But in 6 months time you may want to escalate things to protect this aim, if things develop further. Please be aware your manager has bullied you. She should be scared, not blasé. Futureproof things to give yourself options:
Send the screenshot or whatever to yourself as an email attachment. Along with the email correspondence between you. Send them to your personal email.
Send yourself a personal email about what happened, so you have a contemporaneous record. Imagine you're writing it as a simple statement of your version of events for possible use in an HR meeting. Because it might be.
Repeat the last step again as a separate email (again to your personal account) but this time include emotion. How it made you feel, your anxious concern for your reputation amongst colleagues, etc. You can then choose which one is appropriate to use if required.
Always to your personal email though, in case of a data access request of your work account.
Speaking of which, if things get serious, you could make a data access request of her inbox for anything mentioning your name. This is all just if things escalate, but please futureproof things for now even if you take no action. To protect your future, your pension, your sanity, etc.