It's a little hard to answer this one. Clarify the following first
Thanks for the response, Zeng.
Should I do the same in the new team as well, since it is in a similar mess?
Why not? This is a very common playbook I saw from job switchers. A super common playback is to be at a Big Tech company where most processes/infra are very well refined and then go to a smaller company like a pre-IPO startup to "copy-paste" the infra from the Big Tech company.
The copy-pasta doesn't even have to be technical: After I joined Robinhood, they were looking to add clarity to defining Staff Engineer expectations. The staff engineer persona is something I'm pretty passionate about, so I worked with a principal engineer to define Staff Engineer archetypes into the official Robinhood Engineering Wiki. For the archetypes we added, we pretty much took them from Meta, haha.
Anyways, my point is that if this is a genuine problem and applying your past experience would be good impact, no reason not to do it. I can't imagine being penalized for leverage the prior wisdom you have built: That's sort of the point of bringing on a senior engineer.
Do you suggest is it better to look for an up-level outside of the organisation or stay put? What factors does it depend on?
In general, my logic is as follows: If you like your team and are growing, stay. Otherwise, leave.
In terms of signals to look out for judging growth potential, here's some: