Not nearly the same kind of losses, I don't think. The drop in value of bond-like investments is heavily affected not just by the change in interest rates but also the duration: long duration bonds drop much more heavily because the total amount of interest people now expect over their life is much higher. The interest rates on three-month Treasury bills has barely increased over the last few months (which is obviously the longest they could've been holding any for), and then taking into account the duration and the interest they're receiving they shouldn't be looking at mark-to-market losses at all really.
I agree with your conclusion: holding 3-month t-bills virtually isolates you from interest rate risk.
But not because rates do not change (they do, a lot: for example 3-month rate jumped by over 0.5% in 2 weeks of Oct 2022). But due to the short duration such change barely affects the remaining interest paid by each bill, which is what determines bill's price.
Agree with the first part, short duration implies lower volatility. But we know that T-bills are zero coupon bonds, so holders are not receiving interest payments along the way, the interest is built into the redemption price. So forced selling because of a run for example, at a bad time, can mean a loss on the price and therefore no interest.
Although, still room for losses with those numbers ($50B) https://ycharts.com/indicators/3_month_t_bill, and make them more likely to want to hold to maturity.