[backport#15288] Remove use of g_connman / PushInventory in wallet code

Summary:
6d6bcc77c058fbcfd39c7e3050bbe82fc89024cf This commit does not change behavior. (Russell Yanofsky)

Depends on D5840

This is a partial backport of Core PR15288

Test Plan:

cmake .. -GNinja -DENABLE_WERROR=ON -DCMAKE_BUILD_TYPE=Debug -DBUILD_BITCOIN_WALLET=OFF
ninja check-all
cmake .. -GNinja -DENABLE_WERROR=ON -DCMAKE_BUILD_TYPE=Debug
ninja check-all

Reviewers: #bitcoin_abc, deadalnix

Reviewed By: #bitcoin_abc, deadalnix

Differential Revision: https://reviews.bitcoinabc.org/D5851