To give a different perspective of day in the life of...
I'm a consultant, so unlike OP I am client facing. My reason behind this is because long term Product delivery isn't my cup of tea. I much prefer project based work. Ideally I work with a customer for 1-6 months.
Project work can vary, it can be discovery work, focusing on designing a roadmap for a customer to achieve their "moon shot"/dream. Or it can be a longer project actually building out a platform, or programme for them. As I work mainly with data, it's architecting and building a platform, or implementing specific data processing algorithms, or even getting hands on with some cognitive sevices (image recognition, chat bots etc). That's why I love consultancy, it's very varied.
My day normally starts with doing all my internal admin, and a bit of training. I like to try to do 30 minutes a day of video based learning on Plural Sight. (Not great for beginners, but amazing once your in career or in an area and focused). I then prep my tasks for the day. Join stand ups (I'm normally on 2-3 projects so do one for each). Then start my first task. I spend 75% of my time doing my own tasks and 25% in meetings. I try to group of meetings into the morning or the afternoon so I can get some focus time to do tasks, context switching can completely derail a technical task so I try to minimize it.
Like OP, we do agile project management so effort is focused to particular deliverables over a sprint, lasting 2-3 weeks depending on project.
Best bit is really difficult business problems to address and lovely customers. Worst bit for me is rude customers and long term projects.
Hope that helps anyone watching this thread to know it's a really varied industry.