[backport#15091] Qt: update header count regardless of update delay
Depends on D6177
Partial backport of Core PR15091
In a node that isn't 100% synced, see that overlay describes it is receiving headers,
and then blocks correctly.
Reviewers: #bitcoin_abc, jasonbcox
Reviewed By: #bitcoin_abc, jasonbcox
Differential Revision: https://reviews.bitcoinabc.org/D6179