Hmmm, for me Geany middle click pastes where the pointer is _and moves the caret to the paste location which removes the select_. On Geany 1.36 this still allows pasting even though there is no selection, and the former selection middle click pastes in other apps even if it isn't the selection any more. But with Geany git no further pastes inside Geany or in other apps happen because there is no selection, which is arguably the correct behaviour if the caret is moved and the selection removed.
Other apps I tried (Xed, Gedit, Libreoffice writer) all worked the same as each other, middle click pastes where the pointer is, but the cursor and selection are not modified, so repeated pastes are possible, left click to move the cursor and the selection is removed and no further middle click pastes are possible.
So older Geanys (and Scite 4.3 which I tested) did not behave the way other apps do either. They moved the cursor and de-selected which no other apps do.
AFAICT Geany does not handle the middle click, it happens in Scintilla. I can't build a current Scite ATM to see if it behaves the same as git Geany, if you can build it and find it does, please report it to Scintilla (referring to Scite which is the reference editor for Scintilla). Probably Scintilla should really behave as other apps do, keeping the caret position and select, rather than reinstating the past erroneous behaviour.