Should I give my manager/coworker feedback about the culture of the team?


I(31 F) joined a new team few months ago as an experienced software engineer(7 yrs), but still not at a senior level. Also I work at a company who don’t disclose people’s levels.

So I have an engineer, who has less experience than me, but definitely more in the team (4 yrs).I have some cultural issues I am facing.
The coworker acts as a manager, i.e suggesting work for me and such. I was okay with it initially as I am new. I am also very open to learning from them, as they do have more experience with the stack than I do, and maybe can even teach me something about software engineering they have learnt.

I am wanting to move to next level, for which I was put as a lead on a project. The said coworker were asked to pre-scope the work a month ago, which they did include me in. But since I was asked to lead this, I setup a meeting with them and the manager as sort of kick off and take it from there. They did a lot of scoping work I was supposed to do before the meeting.
I felt pretty bad as that was what I was supposed to do.

Next a couple of months ago doing the task that they had suggested, my QE found a pretty serious bug, I and the QE were involved in mitigating it and fixing the bug. Since it was their bigger area, they led the effort later to form a long term plan to avoid this.
I provided an idea for the same, and they wrote it as something of theirs, and in front of executives, the whole situation was provided as something that ‘we’ did and ‘we’ got an idea that we can work on.

I am considering the best way to stand up to this, should I talk to manager, or the coworker directly. Or not at all!

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