What does “with matters in this recumbent posture" mean?

There are two terms in this paragraph which you may not know:

"Matters" is a fairly common but formal way of referring to what is currently under discussion, for instance you might ask your legal team "How is the case going on?" and they might say "Matters are proceeding slowly at the moment" meaning that they weren't making much progress.

"To be in a recumbent posture" is to be lying back with the upper body slightly supported. However it is an obscure and somewhat pretentious way of saying it and it really only applies to people, not to 'matters'.

To say "with matters in this recumbent posture", therefore, is to use one formal but fairly common term (matters) but to obscure the meaning by saying that they are "in a recumbent posture" instead of saying that nothing much was happening.

"Recumbent posture" has been pretentious language for so long that the early twentieth century English dialect writer Marriott Edgar used it in a comic monologue called The Recumbent Posture. In this a young working class boy's parents are given a bottle of medicine to make him sick after he swallows a gold coin (don't ask why, there is a sort of twisted logic to it) with instructions written on the label that it is to be taken "in a recumbent posture". This confuses the poorly educated parents who then try to borrow or buy a "recumbent posture" from other people who don't know what it means either until a pharmacist says that "it's Latin and means lying down".

EDIT: I've just realised that I mixed up two different Marriott Edgar monologues in my head. The one with the gold coin is The Jubilee Sovreign Edgar was very prolific and I've lead something of a wasted life:-)