test: Properly set sync_fun in NodeNetworkLimitedTest

Summary:
This is a partial backport of core#23474:
https://github.com/bitcoin/bitcoin/pull/23474/commits/fad13991aea6463ecf07dd907de1c1b23837d7e7

Test Plan:

./test/functional/test_runner.py p2p_node_network_limited

Reviewers: #bitcoin_abc, PiRK

Reviewed By: #bitcoin_abc, PiRK

Subscribers: PiRK

Differential Revision: https://reviews.bitcoinabc.org/D12533