If you were in my situation, would you generally assume the company is probably a goner and look elsewhere (even if the product is/could be good)?
You mentioned you are not the founder or have decision making power. In that case, you need to see what the founder(s) feel. If they are ok with mediocrity, it will creep in further. I always say that the team's urgency by default is always 0.5x of the founders. So if the founders themselves are relaxed, it will get worse.
I'm just so frustrated. It's annoying to see what could be a good product get waylaid like this.
And from a selfish perspective, I'm wondering if I should move on now despite only working there for a few months (looks bad on resume) or push through for a while. What would you do?
Ultimately, you should decide what team you want to be part of but don't make decision abruptly either.
Let me guess, a salary that is below market's standards and yet you still expect the best from them.
That only makes you an hypocrite and entitled.
Startups need to execute. Execute Fast. I am not talking 80 hour work weeks but more like getting things done every day, every week, every month. Especially in early days when you don't have real Product Market fit and you are constantly experimenting to figure things out. Mediocre employees won't be able to keep up with that need. Mostly because they can't but in many cases, they don't want to. Also, book smart people can also be mediocre if they are not willing to move the needle.
The first 10-15 hires cannot be mediocre. I don't mean to say that they have to be geniuses IQ wise. But they have to have the same sense of urgency which founders have and they should be able to execute every day. Period. Definitely don't hire from large companies unless they have already shown that they want to work at startups.
Source: I have hired a lot of these "mediocre" types and I don't blame them honestly because it was my fault as the founder. Most have been nice to work with. But just being nice wont get you anywhere. You need to find hungry people who are willing to put the time in, learn and execute fast. Super fast. I could do a whole podcast on hiring mistakes that I have made as a founder. Very expensive mistakes that that cost us not just in terms of money but time to market.