>> Can other GNSS give usable timestamps? Seems like it'd be tricky for a jammer to target all of them

Actually the opposite; GNSS systems are all purposely designed to operate at virtually the same frequency (check out this figure [1]) while cleverly not interfering with each other. There are sub-bands within each constellation too (L1,L2,L5 etc) but it's very easy to pump out wideband noise across all the GNSS bands.

[1] https://www.researchgate.net/figure/The-spectrum-of-current-...