Add LDK Node integration test #2444

Job	Run time
check_docs	3m 20s
build-tx-sync (ubuntu-latest, stable)	3m 32s
build-tx-sync (ubuntu-latest, beta)	3m 33s
check_release	3m 0s
build-tx-sync (ubuntu-latest, 1.75.0)	3m 33s
build-tx-sync (macos-latest, beta)	3m 34s
build-tx-sync (macos-latest, 1.75.0)	1m 17s
rustfmt	14s
build-tx-sync (macos-latest, stable)	1m 19s
linting	2m 23s
benchmark	3m 32s
fuzz	1s
ext-test	1s
build (self-hosted, beta)	3m 20s
build (self-hosted, 1.75.0)	1s
build (self-hosted, stable)	1s
build (macos-latest, stable)	1m 17s
build (windows-latest, stable)	3m 30s
build (macos-latest, 1.75.0)	1s
coverage	1s
	37m 30s

Provide feedback