Shimano freehubs have the freehub body attached to the shell, and the assembly supported on bearings at the ends. If the freehub-hubshell connection is loose it'll present as you describe.
Remove the axle, sirck the big hex hey inside and make sure the internal nut is tight. Or, before you take it fully apart, leave it tight in the frame, push the rim across with decent pressure, and see if you can see deflection behind the cassette (easier to see if the cassette is off). Sometimes you can feel the loose freehub when the cones are backed off slightly.
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