With http, the protocol doesn't indicate where the headers end and the
next transaction or body begin. Until now, we handled that for client
header response parsing by reading from the tls buffer bytewise.
This modernizes the code to read in up to 256-byte chunks and parse
the chunks in one hit (the parse API is already set up for doing this
elsewhere).
Now we have a generic input buflist, adapt the parser loop to go through
that and arrange that any leftovers are placed on there.
