node: Use existing NodeContext

Summary:
This is a backport of core#21270 [7/12] and core#21525 [7/10]
https://github.com/bitcoin/bitcoin/pull/21270/commits/4cde4a701b8856ac4ec9721b0226dbbfc52a71c3
https://github.com/bitcoin/bitcoin/pull/21525/commits/88aead263c61d86e5f836028f517cfbf2a575498

Depends on D11422

Test Plan: ninja all check-all

Reviewers: #bitcoin_abc, Fabien

Reviewed By: #bitcoin_abc, Fabien

Differential Revision: https://reviews.bitcoinabc.org/D11423