I recently bought this H-Bridge to control a 12V actuator with my Arduino, but I’ve realized that this H-Bridge is an “Half Bridge” and not a “Full Bridge”, so I can’t control the direction of the motor and I need my actuator to deploy and retract obviously.
My question is: Is there a way to create a “Full-Bridge” by joining two of them or something like that? And be able to control the direction of my actuator.
I think you bought a single mosfet switch. The 2 mosfets are in parallel. Not even a "half bridge". So you need 4 of them to make a full bridge + extra electronics. It's too much of a hassle so don't bother. Just order the right item on Aliexpress
The item you linked to is not a bridge or even a half bridge nor even listed as a bridge. You cannot make that into a bridge. Buy what you actually need. Look at your actuator current under a load and buy an adequate bridge designed for your intended use.
A full bridge (aka H-bridge) is 4 MOSFETs (= 2 half-bridges).
A 3-phase bridge = 3 half-bridges.
There are many half-bridge driver chips for use with 2 n-channel MOSFETs,
this is the de-facto way to build power electronic circuits. There are some that
can do a full-bridge or 3-phase bridge driving in one chip (but less choice that way).
Checkout IR2001, IR2004, HIP4081A, FAN7388 and such chip's datasheets for lots of detail.