I've onboarded as a senior developer onto a new project few different times: twice at a startup, once at a largish company, once at a very large company, and once at a coming-out-of-startup phase company (that time as a hybrid dev-manager). A few pointers:

1. First thing is to come up with a ramp-up plan. Before you touch any code, before you fix bugs, make sure you have a 30- and 90- day plan for where you need to be and what you need to know. That plan should include with coming up with questions for people and meeting with them to ask them, understanding the company's strategy at a sufficient level, and, yes, understanding the code base and development procedures.

2. As a Senior Developer, it's good to know where the project is now, but people are looking to you to know where the project will be in 6-9 months. So, while fixing bugs is good, don't get bogged down in that - after some initial familiarization, take up tasks that let you focus on big picture architectural and process issues.

3. Take time to get to know your colleagues. Have lunch with them. Have non-work conversations. Start to learn what interests them. Without explicitly asking, pay attention to clues about career goals and what they find challenging. As a senior developer, demonstrating that you are genuinely interested in your colleagues goes a long way towards earning trust and getting embedded into the team faster.

3a. Get a sense of the team's culture. Are there cultural norms you're not used to? Are these norms good/bad/indifferent?

4. Given that you are a Senior Developer, you should make sure your team is hitting a lot of basics. Are there feedback loops, both business-wise and process-wise to your team? If not, you should work on getting these in place (or at least making sure that it happens). Business feedback loops should include some kind of KPI report, adoption report, etc. Process feedback loops usually include regular, honest and constructive retrospectives. Usually if you're hired as a senior developer on a team, most of your teammates will have limited experience in these.

5. Whenever possible, share your perspective. One of the big differences between a senior developer and non-senior developers is that you've seen a few projects, and you've probably seen pitfalls along the way. That's probably a big reason why you were hired. A great way to add value to a team when you still don't know the nitty-gritty is being able to say "It sounds like we're doing X. I was on a team once that did X, and A, B and C happened." Of course, always do it from a point of view of humility - there might be new constraints that you didn't know about.

Beyond that, a lot of it will depend. If you're joining a large company, you should spend some time doing "company networking," i.e. , meeting other senior developers, project managers your team works with, understanding not just your project but other projects near you in the org. If you're joining a start-up, chances are there is a deadline in a few months, so the emphasis will be much more on delivering something immediately. Writing documentation can sometimes be helpful, but if you're at a startup that now has hired its full allotment of engineers, writing a ton of documentation about how to get up to speed is of limited use. Fixing bugs can sometimes be a good approach, but sometimes for teams that didn't have a senior developer before, the proper fix involves a design change. Is there someone else who is also interested in raising the bar for engineering practices, but doesn't know where to begin? Work with that person, since you have the experience as a senior developer, and that person understands the specifics of the team.