Remove usage of last toolType for new startInput

With [1] we migrated to usage of InputManager to determine last used
toolType. We no longer need to rely on previous method of using
lastToolType propagated from handwriting listener.
This change was missed from original change.

[1]: I17b9d7d13e2fa265c0f9b04f1cf7193a1ce86638

Bug: 336615195
Fix: 345102784
Test: atest StylusHandwritingTest
Change-Id: If7716adfdd1958bc49fb764c3fdbded52f034bb6