Keep a server SIV instance for each available algorithm.
Select AES-128-GCM-SIV if requested by NTS-KE client as the first
supported algorithm.
Instead of encoding the AEAD ID in the cookie, select the algorithm
according to the length of decrypted keys. (This can work as a long as
all supported algorithms use keys with different lengths.)
Add a context structure for the algorithm and keys established by
NTS-KE. Modify the client to save the context and reset the SIV key to
the C2S/S2C key before each request/response instead of keeping two SIV
instances.
This will make it easier for the server to support different algorithms
and allow the client to save the context with cookies to disk.