I'd be happy to make the changes to the codebase but there's definitely scope for improvement. Putting a sleep to avoid repeated lock acquisition should have raised an eyebrow or two when it was implemented.
As mentioned, there should be a read-replica specific code that works using event listeners. Repurposing the primary's code is what causes the issue.
The following pseudocode would give a better picture on the next steps
// Read replica specific implementation
void StandbyWaitForTransactionCompletion(TransactionId xid) {
// Register to receive WAL notifications about this transaction
RegisterForWALNotification(xid);
while (TransactionIdIsInProgress(xid)) {
// Wait for WAL record indicating transaction completion
WaitForWALEvent();
CHECK_FOR_INTERRUPTS();
// Process any incoming WAL records
ProcessIncomingWAL();
}
UnregisterForWALNotification(xid);
}