I think there are two important thresholds of productivity here that create three distinct classes of government worker.

Those thresholds are productivity > cost and productivity < 0.

In the rare (perhaps mythical) cases that government workers produce more than they cost, these are just useful jobs that are being done by the government. They'd probably be done better on the market, but they aren't any sort of welfare.

In many cases, government jobs actually do things that make everyone else poorer, on top of the impoverishment of paying for them. These counterproductive jobs may give the employee a sense of purpose, but they're worse than UBI for the rest of us (assuming that people on UBI don't just become criminals).

Then, there's the in-between cases. Government jobs that provide positive value, but less than their cost. I think that's what the little old lady staffing the library is. Those jobs are at least debatably better than a UBI.