There are many directions you can take testing, but just want to understand how to frame the right mindset of "proving" impact for a concept where success is that you prevented or saved risk from the company (no one will know about it essentially if you do your job well).
You have nailed the difficulty behind measuring the impact of automated testing. That being said, it's definitely measurable (just hard to do so):
#1 and #2 require manual labeling unfortunately.
You can go into a lot more depth here: "What do mobile testing strategies look like at top tech companies?"
If you are building out a new testing initiative, it's helpful to gather all of the previous incidents to show that your new initiative could have helped to prevent ~60% of the previous issues.
Moving forward, it's helpful to get a benchmark for how many incidents and their severity before your testing initiative. Then, you can track to see whether the number of incidents and their severity have gone down.