Two circuits with different voltages – should I use a transistor or an optocoupler as a switch

The first choice to make is whether you want to switch the input to the 12 V power supply, or switch the 12 V to the pump. If the pump spends a lot of time off, then powering down everything is probably a good idea. The 12 V supply will take some idle current, which is a waste if the 12 V isn't used for long periods of time. On the other hand, if the pump is on a lot and is turned on and off a lot, it will be easier to switch the 12 V to the pump. You could then even run the microcontroller off of the 12V, perhaps even with a linear regulator if you can keep its current down.

To switch the line power into the power supply, a plain old relay would be the simplest choice. There are plenty of relays that can be controlled from 5V that are intended to switch line power. Your supply will take well under 1 A, so there will be a wide choice of relays.

To switch the 12 V power to the pump, I'd probably use a transistor as a low side switch. Since the 12 V is already isolated from the line, you can tie the - side of the 12 V supply to the processor ground and use a direct connection. Lots of stuff can switch 1 A at 12 V. Here is a simple circuit:

To eliminate any possibility of surprise, and to generally make things more robust, I'd suggest using an optocoupler like 4N25.

^{simulate this circuit – Schematic created using CircuitLab}

With this arrangement, you don't need to worry about how to combine the separate grounds of the two systems, because their grounds simply aren't connected. Also, if there's a problem on either end, the optocoupler may isolate the fault to one side, and is cheap to replace, where a Raspberry Pi or garage remote is not.

Depending on exactly what the garage remote is, you may need to add another transistor to handle additional current, because the 4N25 has an absolute maximum of 50mA. Q1 is one way to do that, and general PNP transistor you can find will work in this application. This arrangement formed by Q1 and the output transistor of the 4N25 is called a Sziklai pair.

One potential disadvantage of this solution is that when the transistor is on, the remote (represented by U1 here) will see only about \$8.2V\$, where it would have seen the full \$9V\$ had these transistors been replaced with a mechanical switch. This is because you lose \$0.6V\$ from the emitter-base drop of Q1, and another \$0.2V\$ from the collector-emitter drop of the 4N25. However, I doubt this will be a problem in practice.