Yes. Normal. But it doesn’t feel good.
My GS500 (110/70 front tire; 130/70 rear tire) would wiggle every time I crossed those longitudinal grooves on pavement. I’m used to the wiggle now, but crossing those grooves still makes me a little nervous about edge trap. The wiggle is less obvious on my SV650, and even less on my YZF-600R. After I changed the tires on the GS500 to Perilli Sports Demon, it seems to get better (less wiggle). I think tire construction (tread pattern, how stiff/soft the sidewall is, bias ply vs. radial) makes the biggest different whether it tends to track grooves on pavement, followed by how good the suspension is in soaking up (damping out) the wiggle. Tires with a continuous, unbroken center groove in the tread pattern tend to track grooves in pavement more than those with alternating tread pattern.