One of the biggest shifts in how I understand the Site Reliability Engineer role was a transition from "SREs take a product and add reliability features to it (monitoring, load balancing, failover, etc.)" to "SREs empower product developers to make their product reliable".
The empowerment comes in many forms: building tools and frameworks, contributing to the product core, participating in design process, documenting best practices and writing postmortems. But one of the most important ways is reaching out to your fellow product engineers, at individual level, and educating them about all you've learned as an SRE. You don't have to have "reliability" in your job title to understand and implement the ideas behind reliability engineering.
Developing technical credibility with your dev teams is what ultimately opens the door to your ability to educate. A few things that worked for me well: make deep technical contributions to the product core, participate in design discussions and show your interest in learning the product's problem space, don't be afraid to ask silly questions, be willing to listen and acknowledge your mistakes.
Or, in other words, if you come across as a seagull who shows up in your design doc comments, shits all over it and calls the author an idiot, people will not like or trust you even if you are technically correct.