I know nothing about RISC-V, but my usual way of finding out how to do something standard with a given instruction set is to ask a compiler. There are online compilers, such as this one: https://cx.rv8.io/ Just type in "__int128 add(__int128 a, __int128 b) { return a + b; }" on the left, stick "-O2" into the "Compiler options", and see what you get! I don't know whether that particular compiler is doing the right thing, of course, but it gives you an idea and it's definitely less work than reading the spec.

No need for branches, see comment above demonstrating sltu.

For a long carry chain, I guess it might look like this:

  ; Inputs: x = 4-word number, in a3:a2:a1:a0,
  ;         y = 1-word number, in a4.
  ; Output: x+y, 5-word number, in a4:a3:a2:a1:a0.
  add  a0, a0, a4
  sltu a4, a0, a4 ; a4 = carry bit
  add a1, a1, a4
  sltu a4, a1, a4 ; a4 = carry bit again
  add a2, a2, a4
  sltu a4, a2, a4
  add a3, a3, a4
  sltu a4, a3, a4

Ah, nice, thank you! I must have missed sltu.