Week three?! You're already complaining about "not having learned a lot"?! are you mental?! Expect to be in receive (vs transmit) mode for the first three to six months before you can become autonomously "effective".
What's the most you would expect to learn in three weeks? Is that really feasible? Wouldn't the world be a different place if it were that easy? No it isn't and yes it would.
To answer your question: create lists of what there is to know and what you already / don't know.. Managers of all abilities love them and they are good for you to use to measure your learning. The more you learn about the firm and its systems, the more understanding you get about what's important and where the frictions lie. The more frictions you can remove the smoother life gets for everyone. Don't be obsessed about "delivering value" out of thin air in the first few weeks. If you must be obsessed about something then "learning everything" is a healthier option.
Working remotely can be difficult at first, depending on the crowd and culture. I joined a firm where I was their first remote-first and remote-only employee, and it was hellish. I put this down to both them and I being equally incompetent in how to work effectively across timezones with and as a new remote-only employee. I suspect many people will have had similar experiences in the past few months. The difference is that when you are a new employee, you don't know anyone, and it's very difficult to build up trust, rapport, and camaraderie with colleagues, and without all three of those ingredients it's no surprise that feelings of anxiety can creep in. Of course, when one is in this situation to begin with, it's difficult be aware of all this, or, when one does glimpse it, it can be overwhelming.
Don't worry. Keep on keeping on, learn as much as you can from the right people. Emulate the learning practices of the longest-serving, and most successful colleagues as you identify them. Ask them for their advice or suggestions as to what they think would be the best subject matter for you to become an expert on. Ask them what (relevant) books they'd recommend -- and read them, especially the ones others don't. You'll find you learn a lot about people (and more importantly who to avoid) by the authenticity of their advice.
There are edges to be had everywhere.