[gui] send dialog: split on_sendButton_clicked

Summary:
This commit does not change behavior.

Backport of Core PR17509 part [1/6] : https://github.com/bitcoin/bitcoin/pull/17509/commits/6ab3aad9a51cc5e97a8e2ae7dbd5082272163c30

Test Plan:

ninja all check-all

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Differential Revision: https://reviews.bitcoinabc.org/D8066