[bug]: close channel can be stuck

[yyforyongyu]

From this build,

Error Trace:	/home/runner/work/lnd/lnd/lntest/harness_assertion.go:471
            	            				/home/runner/work/lnd/lnd/lntest/harness.go:1310
            	            				/home/runner/work/lnd/lnd/itest/lnd_mpp_test.go:532
            	            				/home/runner/work/lnd/lnd/itest/lnd_amp_test.go:476
            	            				/home/runner/work/lnd/lnd/lntest/harness.go:303
            	            				/home/runner/work/lnd/lnd/itest/lnd_test.go:130
            	Error:      	timeout
            	Test:       	TestLightningNetworkDaemon/tranche05/189-of-276/bitcoind/send_payment_amp
            	Messages:   	timeout waiting for close channel update sent

It seems sth is blocking by looking at the timestamps,

2025-03-25 04:37:09.751 [DBG] RPCS interceptor.go:791: [/lnrpc.Lightning/CloseChannel] requested
...
2025-03-25 04:37:10.039 [DBG] DISC gossiper.go:857: Processing remote msg *lnwire.ChannelUpdate1 from peer=[Bob]
2025-03-25 04:37:10.039 [DBG] DISC gossiper.go:2952: Processing ChannelUpdate: peer=[Bob]@127.0.0.1:11589, short_chan_id=[SID: carol=>eve], 
2025-03-25 04:37:10.039 [DBG] DISC gossiper.go:3020: Ignored stale edge policy for short_chan_id([SID: carol=>eve]): peer=[Bob]@127.0.0.1:11589, msg=ChannelUpdate, is_remote=true
2025-03-25 04:37:33.895 [INF] GRPH builder.go:825: Processed channels=6 updates=22 nodes=22 in last 1m48.843781063s
2025-03-25 04:37:38.790 [DBG] BTCN broadcaster.go:236: Re-broadcasting 2 transactions
2025-03-25 04:37:44.965 [DBG] HLCK healthcheck.go:330: Health check: chain backend invoking success callback
2025-03-25 04:38:38.789 [DBG] BTCN broadcaster.go:236: Re-broadcasting 2 transactions
2025-03-25 04:38:40.111 [INF] PEER brontide.go:2017: Peer([Bob]): unable to read message from peer: read next header: EOF
2025-03-25 04:38:40.111 [DBG] PEER brontide.go:1589: Peer([Bob]): Started, waiting on startReady signal
...
2025-03-25 04:38:40.671 [INF] LTND lnd.go:152: Shutdown complete

Full logs can be found here.