What happens when a new PPP packet is sent while the server is still processing another packet?
Does it simply get queued and blocked if the server's incoming buffer is full?

For example, something that can't be replied to immediately (like the buffer for the other direction is full, or some action that takes time (like authentication or address assignment that requires negotiation on the network, like DHCP or ARP on said server))?

UniPCemu's server currently just blocks incoming packets (of any kind) until it's processed the incoming packet from the client, effectively halting the serial communication in the server's direction. The same is true if it's still sending a packet to the client when it receives a packet from the client that tries to send a packet back to the client (like an ACK of any kind).