Powering a RPi and a motor driver with the same LiPo battery
I think it should work. One thing to note is that 7.4V is a nominal voltage for a 2-cell LiPo battery. The full range of the battery voltage (depending on its charge status) is something like 6.6V - 8.4V (3.3V - 4.2V per cell). So the voltage regulator you linked may not be appropriate - its spec list only 7V as an input.

You may want look for a low-dropout voltage regulator. Alternatively, you can try using a DC-DC converter for better efficiency. E.g.

https://www.pololu.com/product/2858

Also, you can look around for a 5V BEC (UBEC) (Battery Eliminator Circuit) used for RC models. E.g.

https://www.adafruit.com/product/1385
https://www.aliexpress.com/item/Hot-Sale-DC-DC-Converter-Step-Down-Module-UBEC-3A-5V-12V-BEC-For-RC-Airplane/32824894112.html
(many BECs on Amazon)

In any case, you do want to make sure that once you apply full power to DC motors, the battery voltage does not drop below the minimum regulator value.

DISCLAIMER: I never actually powered RPi3 or any Single-board computer this way: not providing any guarantees.

For the reference:
When to use multiple batteries vs a UBEC