Traditionally, pasting into terminal emulators used to be nothing more than pretending that the user quickly type the given letters from the keyboard. Combined with the autoindent feature of many editors (e.g.
nano -i), if the pasted (pseudo-"typed") text contains spaces or a TAB at the beginning of each line, this obviously results in increasing indentation, that is, the so-called staircase effect that you see.
One possible way to avoid this is to disable autoindent for the duration of pasting. Consult
nano's documentation to see if it's possible to toggle this setting runtime, I don't know.
Recently most terminal emulators have introduced "bracketed paste mode" to improve this situation. This is a special mode that applications (e.g.
nano) might enable, and instructs the terminal emulator to enclose the pasted text between special control symbols. One of the main intents is for text editors to automatically disable autoindent when this happens, that is, to avoid the staircase effect. At this moment I can't see any sign of
nano supporting this. The feature request is filed here, maybe you could ask the developers if they're planning to address this.