Is it normal to feel exhausted after a work day, or am I approaching it wrong?

... but reading code takes up more time than I’d like, as I try and figure out what the service is actually doing, not only in terms of code but in the context it’s meant to be used in- It’s a systematic hedge fund and finance is new to me.

To me, this screams you should ask your teammates more questions. 2 months is still fairly new. It's not reasonable expect the newbie (who's an earlier-in-career engineer as well) to just quickly absorb an entire space they're not familiar with. Check out our video on how onboarding gives you special powers for more on this topic.

Often I feel mentally and physically exhausted heading home from work.

From that last part, it seems like you're going into the office: It's really important to make the most of that, especially if you're new or a more junior engineer (and you're both!). Here's some resources on how to do that.

• Pair program - In-person pair programming is one of the most fun and effective learning things you can do, and it builds up relationships as well. Check out my in-depth thoughts on pair programming here.
• Socialize with teammates more - One of the best ways to mitigate burn out is to have fun, and one of the best ways to have fun is to make friends. Here's my advice on how to make awesome work friends in an in-person environment.