I noticed that "new tasks" appeared after I thought I completed stage 1.

[vivid mauve]

When I did actually complete them (I was at stage 2), they didn't give me the research points or blueprint points.

I know what happened. I actually did compelte the task but for some reason it shows as not complete

[cold kiln]

So I tested this and it seems you can still "claim" and mark them as completed afterwards.
The task is visible before it is unlocked, and you already delivered the required amount, so the vortex counts these already.

I guess we could improve the task unlocking to not let you work on tasks currently "locked".

[fiery zealot]

🚑 Your bug report has been verified and is now in the triage phase. We're working to reproduce and fix it.