Digging further, it does appear that the initially bootstrapped master is broken somehow:
```
2023-05-07 15:06:46 0 [Warning] WSREP: Quorum: No node with complete state:

	Version      : 6
	Flags        : 0x1
	Protocols    : 2 / 10 / 4
	State        : NON-PRIMARY
	Desync count : 0
	Prim state   : NON-PRIMARY
	Prim UUID    : 00000000-0000-0000-0000-000000000000
	Prim  seqno  : -1
	First seqno  : -1
	Last  seqno  : -1
	Commit cut   : -1
	Last vote    : -1.0
	Vote policy  : 0
	Prim JOINED  : 0
	State UUID   : c91ea93c-ece8-11ed-bcbd-d37542ae8d5e
	Group UUID   : 00000000-0000-0000-0000-000000000000
	Name         : 'mgr02'
	Incoming addr: '10.217.122.12:3306'

	Version      : 6
	Flags        : 0x2
	Protocols    : 2 / 10 / 4
	State        : NON-PRIMARY
	Desync count : 0
	Prim state   : SYNCED
	Prim UUID    : 5d5b432a-ece8-11ed-9285-be6bf8d043bf
	Prim  seqno  : 4
	First seqno  : 1
	Last  seqno  : 4
	Commit cut   : 0
	Last vote    : -1.0
	Vote policy  : 0
	Prim JOINED  : 1
	State UUID   : c91ea93c-ece8-11ed-bcbd-d37542ae8d5e
	Group UUID   : 78a25580-ece7-11ed-863d-5af2d3394150
	Name         : 'mgr00'
	Incoming addr: '10.217.122.10:3306'
```
^^ is what happens after the replication error on initial bootstrap of a slave, and that slave is restarted

The donor, being restarted after the two slaves fail to come up, is aware of them but can't figure out which one is primary:
```
023-05-07 20:47:51 0 [Note] WSREP: STATE EXCHANGE: got state msg: 6f57006e-ed18-11ed-9165-5f46e7399b53 from 1 (mgr00)
2023-05-07 20:47:51 0 [Warning] WSREP: Quorum: No node with complete state:

	Version      : 6
	Flags        : 0x1
	Protocols    : 2 / 10 / 4
	State        : NON-PRIMARY
	Desync count : 0
	Prim state   : PRIMARY
	Prim UUID    : cc9462f9-ed16-11ed-8544-d3da5d985617
	Prim  seqno  : 5
	First seqno  : -1
	Last  seqno  : 5
	Commit cut   : 0
	Last vote    : -1.0
	Vote policy  : 0
	Prim JOINED  : 1
	State UUID   : 6f57006e-ed18-11ed-9165-5f46e7399b53
	Group UUID   : 2d143fa4-ed15-11ed-b1b9-03a39ef3932a
	Name         : 'mgr01'
	Incoming addr: '10.217.122.11:3306'

	Version      : 6
	Flags        : 00
	Protocols    : 2 / 10 / 4
	State        : NON-PRIMARY
	Desync count : 0
	Prim state   : NON-PRIMARY
	Prim UUID    : 00000000-0000-0000-0000-000000000000
	Prim  seqno  : -1
	First seqno  : 1
	Last  seqno  : 5
	Commit cut   : 5
	Last vote    : -1.0
	Vote policy  : 0
	Prim JOINED  : 0
	State UUID   : 6f57006e-ed18-11ed-9165-5f46e7399b53
	Group UUID   : 2d143fa4-ed15-11ed-b1b9-03a39ef3932a
	Name         : 'mgr00'
	Incoming addr: '10.217.122.10:3306'

	Version      : 6
	Flags        : 00
	Protocols    : 2 / 10 / 4
	State        : NON-PRIMARY
	Desync count : 0
	Prim state   : PRIMARY
	Prim UUID    : cc9462f9-ed16-11ed-8544-d3da5d985617
	Prim  seqno  : 5
	First seqno  : -1
	Last  seqno  : 5
	Commit cut   : 0
	Last vote    : -1.0
	Vote policy  : 0
	Prim JOINED  : 1
	State UUID   : 6f57006e-ed18-11ed-9165-5f46e7399b53
	Group UUID   : 2d143fa4-ed15-11ed-b1b9-03a39ef3932a
	Name         : 'mgr02'
	Incoming addr: '10.217.122.12:3306'

2023-05-07 20:47:51 0 [Warning] WSREP: No re-merged primary component found.
2023-05-07 20:47:51 0 [Warning] WSREP: No bootstrapped primary component found.
2023-05-07 20:47:51 0 [ERROR] WSREP: ./gcs/src/gcs_state_msg.cpp:gcs_state_msg_get_quorum():947: Failed to establish quorum.
2023-05-07 20:47:51 0 [Note] WSREP: Quorum results:
	version    = 6,
	component  = NON-PRIMARY,
	conf_id    = -1,
	members    = 0/3 (joined/total),
	act_id     = -1,
	last_appl. = 5,
	protocols  = -1/-1/-1 (gcs/repl/appl),
	vote policy= 1,
	group UUID = 00000000-0000-0000-0000-000000000000
2023-05-07 20:47:51 0 [Note] WSREP: Flow-control interval: [28, 28]
2023-05-07 20:47:51 0 [Note] WSREP: Received NON-PRIMARY.
```

This happens whether haproxy is enabled or not, ditto proxysql.