Although as a counterexample for the software version showing FSD Beta or not, it seems like 2022.8.10.20 switched back to just "v11.0" even though I would guess it was still FSD Beta 10.69.3.3 (i.e., not single stack highway v11):
But 2022.8.10.15 did still show it as FSD Beta 10.69.3.3: