handlePaste

Handles request immediately or retains it for deferred completion.

Hosts own clipboard access, consent, and asynchronous work. Read the captured source, then call SwingTerminalMiddleClickPasteRequest.complete on the EDT, or SwingTerminalMiddleClickPasteRequest.cancel to decline. Callback failures cancel unresolved completion and propagate unchanged. An already admitted paste cannot be retracted if the callback subsequently fails.