[bug]: Alice forgets about her own private channels when routing a circular payment back to herself through Bob

[ZZiigguurraatt]

Consider the following scenario:

           TAP
 Alice <---------> Bob
           SAT
        (private)

where Alice and Bob both have allow-circular-route set.

If Alice tries to pay an invoice to herself with AllowSelfPayment: true, it doesn't route the payment unless she also has Private: true when running AddInvoice.

Alice should be smart enough to know about her own private channels with Bob without needing the Private flag set to true. Especially since taproot asset channels are currently always private channels. We really need Alice to be able to not have to think or even know that those taproot asset channels are private channels and still be able to use them as if they are normal channels, because to her they should be no different than a public channel since they are her channels.

Why would Alice ever want to make such a circular self payment?

1. As a workaround to [feature]: allow settlement of an invoice to yourself without routing the payment #7419
2. If the channel between Alice and Bob is also a taproot assets channel and Alice wants to trade a taproot asset for sats with Bob, without routing through any other nodes.

[ZZiigguurraatt]

Also, in the following configuration, when Bob creates an invoice with Private: true, hop hints to Alice and Dave are not included because of

lnd/lnrpc/invoicesrpc/addinvoice.go

Lines 643 to 664 in 09b6745

	// To ensure we don't leak unadvertised nodes, we'll make sure our
	// counterparty is publicly advertised within the network. Otherwise,
	// we'll end up leaking information about nodes that intend to stay
	// unadvertised, like in the case of a node only having private
	// channels.
	var remotePub [33]byte
	copy(remotePub[:], channel.RemotePubkey.SerializeCompressed())
	isRemoteNodePublic, err := cfg.IsPublicNode(remotePub)
	if err != nil {
	log.Errorf("Unable to determine if node %x "+
	"is advertised: %v", remotePub, err)
	return nil, false
	}
	if !isRemoteNodePublic {
	log.Debugf("Skipping channel %v due to "+
	"counterparty %x being unadvertised",
	channel.ShortChannelID, remotePub)
	return nil, false
	}

, so there is no way for Bob to do a circular payment back to himself through either of them. Bob can only do a circular payment back to himself through Charlie. However, Bob's channel with Charlie is not a taproot assets channel, so Bob can't do a direct trade of a taproot asset for sats.

           TAP
 Alice <---------> Bob <---------> Charlie <---------> Frank
           SAT      ^      SAT                 SAT
        (private)   |    (public)            (public)
                    |
                    |   ⏜
                    |   p
                    |   r
                   T|S  i
                   A|A  v
                   P|T  a
                    |   t
                    |   e
                    |   ⏝
                    |
                    v
                  Dave