I am definitely a spiritual brother with you because I love optimising things. But I am very unsure how do I even start a side career with that premise.
Any advice?
Spend a lot of time with funded startups. Meetups, conferences etc. They will be happy to talk about this. But also online; you need to 'dox' nicks some times, but when you see quite broad questions in slack/reddit about performance of systems and you find out this is some (tech) (co-)founder you can ask them to help. I do no-cure-no-pay if the system is an MVP and crud; I do no-cure-still-pay if the system is larger and already live. That is not because I want to blackmail the company (and if I like the idea you can give me a % as well instead, all fun and games), but usually because 'wanting to help' is punished when it's 'free' as in no good deed will go unpunished. I Did no-cure-no-pay with optimising (and other services) live systems in the past, but as soon as I touch it, people blame me for all kinds of dataloss (while i'm very careful and absolutely make (offsite) backups always) and other misery. So when basically what I do is connect with (co)founders who are in a jam and when they don't have production data yet, I will go no-cure-no-pay; when they have production data they need to keep, I will explore but if I cannot do anything (for that price, mind you; there is always something to do), I still get paid.
There are probably literally 1m projects and growing at any time in this world that have serious issues and that are burning money and that will crash (all the time or sooner or later) that need help. For instance, I know of a large state own postal/courier tracking system that crashes under load every 48 hours. We tried to help them but they are fine just rebooting (manually!). Fine, that happens too.