One of the biggest mistakes I see people make when they're trying to climb out of low elo

It has nothing to do with in-game performance. It's when people in low elo try to play every role, try to play carry style champions and end up just feeding or performing poorly.

Want a good tip to help you climb and improve? Select a role to main and become at least decent at support (it doesn't take much mechanical skill outside of Thresh so it's a matter of at least understanding match-ups). Pretty much everyone at one point or another will get forced to support but very rarely will you get forced to ADC If you srent an ADC main, mid if you aren't a mid main and top of you aren't a top main.

After you select a role, focus on a certain style of champions. Do you play hard carry champions that are focusing more on damage and/or diving? Do you play better with a more utility based champion for peeling or starting fights and generally being disruptive. Select a small pool of champions to become good at that fits your playstyle then focus on your gameplay and what you can perform better at each game. This, by far, is the most effective way to climb and helps you improve as you're climbing. Whenever you aren't climbing, focus on playing other roles to at least have 1-3 champions in all roles in the rare occurance you get forced into a role that you're not good at that isn't support.

I'm not trying to insult good support players either, but the position is by far the least demanding mechanically of any role (but has a very deep level of knowledge required to perform well in the higher you get). It's just that in lower elo, even in higher elo, as long as you play smart, you won't be feeding and you aren't auto losing 2v2 lanes which often lose the game. Give your team a chance to help you out when you're matched up against a good support.

The other point I'm making here is that I see people with 50+ champions played and that's hard to maintain consistency with if you aren't highly skilled and don't have the time to constantly practice that (I don't even have time to do that tbh). It's better to try and have this approach from the beginning because this enables you to lay out a foundation for you to be successful on once you get going in ranked and start climbing and you can build off this.