Flatten always scares me with regards to scalability, thus I prefer

Append @@@ # & /@ Thread /@ Transpose[{aa, t}]

Here probably the same question: How to insert elements of a list into list of lists?

MapThread[Flatten /@ Thread[{##}] &, {aa, t}]

{{{a, b, x}, {c, d, x}, {e, f, x}}, {{1, 2, z}, {3, 4, z}, {5, 6, z}}}

I renamed the a and b on the left side to avoid recursion and used rules to perform the transformations. Look up Rule, and Replace for more insight.

Kind regards, David

In[1]:= aa = {{{a, b}, {c, d}, {e, f}}, {{1, 2}, {3, 4}, {5, 6}}};

In[2]:= t = {x, z};

In[3]:= bb = {
  aa[[1]] /. {e1_, e2_} -> {e1, e2, t[[1]]},
  aa[[2]] /. {e1_, e2_} -> {e1, e2, t[[2]]}
  }

Out[3]= {{{a, b, x}, {c, d, x}, {e, f, x}}, {{1, 2, z}, {3, 4, z}, {5, 6, z}}}