I can speak as someone who went down this path and is now an organizer with the PSL. The process of joining a serious socialist org is definitely different from the DSA's big tent approach. They're making sure you're a good fit for each other and there's no red flags because you'll be a representative of the party.

We send our applicants the party program and a few articles that we then discuss. Education is important so we strike a balance between theory and action. So when you join there may be something like classes but at least in my org most of the time is spent doing work on the ground.

It sounds like you want to avoid joining a reading group. How did you decide on which orgs to apply to? Do they have a social media presence where you could see the organizing work that they're doing? You should think of this as a two-way street rather than a job interview. They should be happy to talk with you about the work that they're doing and I'm sure would like to hear what you're interested in getting involved with. There's definitely organizing work you can do as an applicant. One thing our branch does is to get applicants to attend outreach with party members. And if the org doesn't do outreach, that's not a good sign in my opinion.

I'm glad that you're wanting to get more involved and take action. We need all the people like that we can get!