  We construct symmetric pairs for Drinfeld doubles of pre-Nichols algebras of
diagonal type and determine when they possess an Iwasawa decomposition. This
extends G. Letzter's theory of quantum symmetric pairs. Our results can be
uniformly applied to Kac-Moody quantum groups for a generic quantum parameter,
for roots of unity in respect to both big and small quantum groups, to quantum
supergroups and to exotic quantum groups of ufo type. We give a second
construction of symmetric pairs for Heisenberg doubles in the above generality
and prove that they always admit an Iwasawa decomposition.
  For symmetric pair coideal subalgebras with Iwasawa decomposition in the
above generality we then address two problems which are fundamental already in
the setting of quantum groups. Firstly, we show that the symmetric pair coideal
subalgebras are isomorphic to intrinsically defined deformations of partial
bosonizations of the corresponding pre-Nichols algebras. To this end we develop
a general notion of star products on N-graded connected algebras which provides
an efficient tool to prove that two deformations of the partial bosonization
are isomorphic. The new perspective also provides an effective algorithm for
determining the defining relations of the coideal subalgebras.
  Secondly, for Nichols algebras of diagonal type, we use the linear
isomorphism between the coideal subalgebra and the partial bosonization to give
an explicit construction of quasi K-matrices as sums over dual bases. We show
that the resulting quasi K-matrices give rise to weakly universal K-matrices in
the above generality.
