Backlash at the handwheel will be greater since there are two lots of backlash involved, backlash between pinion and rack and backlash between the handwheel gear and that driving the pinion.
To make matters worse. the pinion /rack backlash will appear to be increased by the handwheel / gear ratio.
BUT, quarter to half a turn of the Handwheel is excessive, and suggests that there may be another problem.
On my lathe, the gear within the Saddle is pinned to the shaft carrying the pinion. If this pin has been sheared, the lack of security may account for the excessive backlash seen.
If this is the case, the Apron will need to be removed from the Saddle, for investigation and repair.
On my lathe, the Apron is quite heavy, so the procedure is Thanks to Geoff Halstead:
Remove one of the capscrews at each end of the saddle, and replace by a length of (In my case M8 
studding with a nut on top.
Slacken the remaining capscrews, and tap with a mallet ro push the Apron off the rollpins locating Apron to Saddle., before removing the capscrews.
Slackening the nuts on the studding will allow the Apron to be lowered gently onto a block of wood, after which the studding can be removed, ready for replacing the Apron.
The internals of the Apron can now be investigated.
From memory, the pin securing the gear to the pinion shaft was 5mm, (yours may be different ) and will need to be driven through and out of the shaft.
Once separated, burrs /bruising on the shaft and in the gear can be stoned off so that gear and shaft are once again, a good smooth fit.
On my lathe, the pinion shaft was not of a particularly good grade of steel, so the complete assembly was replaced by a shop made 1.5 Mod gear Loctited and pinned onto a silver steel shaft.
The repaired Apron was filled with oil, and lifted back into place by using the studding and nuts, until the capscrews provided the final security.
HTH
Howard Fat fingers strike again!
Edited By Howard Lewis on 01/10/2021 13:31:38