Caused a SEV - Publish RCA?

In my 3rd week at Big Tech, I was over-eager to get my first PR merged (into a particular legacy Airflow repo) so I could complete my first ticket and show some progress. I made probably the most classic rookie-mistake of not properly testing my code in staging, and my code ended up causing a sev that took down Prod for about 30 minutes. Since this was a particular legacy Airflow repo, it wasn't the end of the world since only internal workers were affected, only a small subset of the company, and it happened at night. Still, this was a pretty bad look for me to my manager and I've been working hard since to make a better impression.

At my company, for every sev, there's a process to write up a Root Cause Analysis (RCA) Doc where you describe the issue, 5-whys for why it happened, the timeline for how it happened, who it affected, and a few other details. There's technically an SLA of 2 weeks set to each RCA, but looking at other RCA docs, I see a lot of them were never actually filled out.

From my perspective, the reason for the sev was simple: I didn't adequately test in staging. The oncall guy who helped me navigate the issue encouraged me to not personalize it as much and to think in terms of the process, e.g. testing in staging should have been required or canary testing in prod should have caught and rolled back my code.

I have filled out the RCA doc on Confluence and can publish it but am hesitant to do so because I'm concerned about reminding people that I caused the sev.

I have 2 concrete questions:

1. Should I publish the RCA? I can prob get away without doing it since it doesn't look like it's enforced. I guess if someone does decide to follow up and sees I haven't filled it out it could be a bad look, but given that it's been over a month since I was supposed to publish it, it doesn't seem likely.
2. If I should publish, should I look to engage with my oncall mentor regarding implementing some of his feedback for making testing in staging required or canary rollbacks? It seems like a lot of work to do (for myself or others) for something that was a "me-error" and people might get annoyed if they now have to test everything in staging when they don't currently have to. It also takes me away from my current tickets (which my manager prob cares more about me completing).

Thank you for reading this!