3.3V supply and GND are needed for your board to work.
For a ST-LINK debug connection
- GND, SWCLK, and SWDIO are minimum
- reset (NRST) is optional and useful, see below
- SWO is optional and maybe useful. SWO is a fast tracing output which can be used for printf tracing (logging) similar to a VCP_TX but using a different protocol and needing a SWO capable debugger/logger
- VCP_RX and VCP_TX is a useful serial console interface which can be used for printf tracing (logging) as well as for user IO as you like. It can be routed to any USART on your PCB and is not closely related to SWD, just happens to show up on the same USB. Shows up as a COM port on the host PC.
> What about a reset ? i thought, the debugger has to tell the MCU ro reset ? (after flashing)
A MCU reset can also be triggered by some magic SWDIO+SWDCK commands. But this is "soft" and works only when the SWD interface is available, i.e. SWD pins are not reconfigured and MCU not in certain low-power modes. The NRST can give it a "hard" reset anytime, which is more powerful.
Take a look at the broken-off of your Nucleo-64-p board (User manual UM2206). It has GND, SWCLK, SWDIO, NRST, SWO on pin 2-6 of CN3 and VCP_RX and VCP_TX on the connector nearby. You cannot fail if you make those signals available on your board.
CN3 Pin 1 marked VDD_TARGET is a special case. It is an input to SWD for detecting the target (debuggee) VDD voltage which can be evaluated by the debugger. High-end debug probes can use that pin for IO level conversion, galvanic decoupling etc.. Think of it as a 1-channel digital voltmeter input. Maybe useful to connect too, especially to detect low battery... scenarios.
Beware: some low-cost ST-LINK debug clones have a 3.3V pin which acts as an output to power the target, this is not the standard, do not connect.
STM AN4989 Application note "STM32 microcontroller debug toolbox has valuable info on debugging, SWO etc..