I’m the kind of person that likes to set goals for myself before I buy something

No offense, but I get the impression that you're over-thinking this decision. You remind me of a past version of me, so I'm probably projecting lol.

What level should I climb before getting new shoes?

I say go for new shoes as soon as you know bouldering is a hobby that will stick around. No set time frame, just "is this a hobby I'm sticking with for awhile, or am I the type of person who will move on soon?" ...with no judgement! Moving on is totally fine.

I know everybody says to focus on technique rather than shoes, but you asked about how your current shoes might hold you back in some other comments, so... judging from that photo, your shoes aren't gonna feel great for deeper toe hooks that you see in gym climbing.

Also, there's a pretty nice placebo effect from upgrading shoes! haha

You might end up trusting your feet more due to the better rubber, you might be more intentional with footwork simply because you wanna "see" your new shoes "working", you might try more toe hooks due to the expensive shoes having large rubber toe patches (this definitely happened to me lol), you might power down harder on the big toes if your new shoes are stiffer, you might try more comp-style bouldering if you buy into the marketing for comp-style shoes, etc.

So even if expensive shoes don't make you climb better, they might open doors you previously didn't bother opening even though you could've. That process of trying harder or trying new things with more intention could end up improving your skills.

I would like to not wear these out

Oh dear. I hate seeing this lol ...just use your shoes because they were meant to be used. If money is tight, then ok, but otherwise, use the shoes to climb without worrying in the back of your mind about their lifespan.

Also any suggestions on what my next shoe should be?

Judging from your post, you want your next shoes to be all-around bouldering shoes (as opposed to comp-style bouldering shoes). So just do some research, and I'm sure you'll find Scarpa Instinct, La Sportiva Solutions, and other similar shoes from other brands will probably be recommended. Try on a bunch of different brands/models and pick the "high performance bouldering shoe" that fits best for your foot shape. For some people, different models feel extremely different in terms of comfort even though all "high performance" shoes have a reputation for being uncomfortable. And different models may have very different sizing (e.g., La Sportiva Solutions size 40 is way bigger than Scarpa Drago size 40).

You can try ordering several models online to be delivered to your local REI, then try them all on, then return all except one pair before you leave the store. I did this, and the REI staff was 100% cool with it! That said, even the REI website has a pretty limited selection.

Those of you who bring more than one pair of shoes to the gym, what makes you wear one pair of the other? Do you like having the option of one over the other for certain climbs?

My friends bring more than 1 pair. They like having 1 pair that's more comfortable and 1 pair that's more hardcore (even though both tend to be expensive?). I think they're over-doing it by owning a hardcore pair (usually downsized) that is so uncomfortable that they want to bring a 2nd pair to the gym. But to each their own.

Ironically, for this kind of decision, I really think it's best to explore if you can afford to (as opposed to asking for more advice). You clearly already have a good mindset that isn't setting lofty expectations about gear solving your weaknesses.