Remove direct bitcoin calls from qt/bitcoingui.cpp

Summary:
Partial backport of Core PR 10244
https://github.com/bitcoin/bitcoin/pull/10244/commits/3d619e9d3658e36cba4a19a5bed33e5538317b27
Progress towards T417
Depends on D2814

Test Plan:

make check
bitcoin-qt # sanity checking

Reviewers: deadalnix, Fabien, #bitcoin_abc

Reviewed By: deadalnix, #bitcoin_abc

Differential Revision: https://reviews.bitcoinabc.org/D2815