has anyone a solution to turn off the PCD8544 display by software?
After checking the datasheet, writing the "FUNCTION SET" command byte with the P(ower) D(own) bit set, ie. 0x24 to it should do that**. (Write 0x20 to wake it up in horizontal addressing mode).
that applies to the display only. If you also require the backlight to be turned off/on that depends on the physical interface. FWIW, see some examples here:
http://www.cpmspectrepi.webspace.virgin ... Lvspi.html
http://www.cpmspectrepi.webspace.virgin ... lcdV2.html
http://www.cpmspectrepi.webspace.virgin ... dCacc.html
Still running Raspbian Jessie or Stretch on some older Pi's (an A, B1, B2, B+, P2B, 3xP0, P0W, 2xP3A+, P3B+, P3B, B+, A+ and a B2) but Buster on the P4B's. See: https://www.cpmspectrepi.uk/raspberry_pi/raspiidx.htm