I need to use a ESP32 WROVER B based MCU board with a standard (cheap) one-channel 5V relay (e.g. to switch on a mains-power appliance). Attempted removal of excess solder around the headers permanently disabled the 5V power output line from the board (to power a relay or other modules); but other pins functional/board boots up correctly. So at present, there is only a 3.3V power source and 3.3V GPIO pins (and others such as for external microphone and speaker). I assume it is safe to connect a 3.3V GPIO from the MCU to IN and external 5V power source to VCC ad GND of the relay and connect the grounds of the MCU AND relay together to complete circuitry. The relay only needs to switch the appliance on when triggered (for example a lamp) and switch off when triggered again. I have a 3.3 ↔ 5V bidirectional level shifter, but don't think it is suitable here (unless it can be incorporated directly). An alternative may be is to use an arduino uno to connect with the relay, itself triggered by the ES32 and more complex circuitry (bearing in mind the ESP32 GPIO is 3.3V and arduino 5V).
Assuming a relay module: check if it is OK to drive it with 3.3V logic when it is on a 5V power supply, or show the specs for us to look at.
Driving a relay module with 3.3V logic is unlikely to harm the ESP32, but it may not drive the relay properly if the relay module expects 5V logic.
Generally, I would even prefer using an external power supply rather than the 5V pin on a microcontroller board to power a relay module.
As long as you connect everything as you describe, it should work just fine (if the relay module accepts 3.3V logic).
These "digital relay" modules are available in 3.3V and 5V versions. Simply buy one of the 3V models. Here is one, for example: https://www.dfrobot.com/product-1572.html