That's partly because we are discussing productivity growth. Today's productivity growth is on top of the substantial productivity improvements that have been compounding due to past booms like the Computer and Internet one. So in relative terms the growth looks modest, but in absolute terms this is substantial.
Also that BLS chart is a bit unhelpful because it shows time periods covering multiple years and does not isolate the years after ChatGPT launched, which is what the St. Lous Fed looks at and finds interesting indications. Like currently productivity growth is 1.3 percentage points above what was forecasted just before ChatGPT was released. This discrepancy is not fully explained by other factors and lines up with other data sources related to the effects of AI.
The letter you linked is relevant, but it is trying to make a much broader point than I am. Note that:
1) it's asking whether we have entered a "high-growth regime" meaning a period of sustained productivity growth, and itself points out that it necessarily requires years to play out; and
2) its point of reference is the 90s when the computer revolution had truly kicked in after almost two decades of adoption starting in the mid/late-80's, during which any impact was famously hard to find: https://en.wikipedia.org/wiki/Productivity_paradox
So what is astounding is that the effects of the AI revolution may be visible in national-level economics data after only 2 - 4 years since the technology was introduced, and we're already wondering if we have shifted into a "high productivity growth era"!