How to safely run power out to pond pump?

Yes, you're going to want to run either a direct-burial cable or a conduit in a trench from your home to the pond. You'll also want to pull a permit for this work even if you plan to do it yourself and be sure you understand the code requirements in your location so that you don't make an expensive mistake and have to pull it out and re-do the work.

The extension cable or almost any method would be fine if you made sure the circuit has GFCI protection.

Now, GFCI isn't just a different style of receptacle. It is actually a zone of protection. Obviously, it protects things plugged into the plugs (including extension cords), but it also protects any downline wiring that is attached to the GFCI's "LOAD" terminals. That is the single and only purpose of the LOAD terminals, and they should never be used for anything else.

So a run to the pond, through the flood waters, can be done safely by having that wiring be downline from a GFCI. Mind you, the GFCI will very likely trip during flood conditions, but you just reset it after it dries out.

If you saw video of the flood in Houston last? year, you saw many, many 2-story apartments with the first floor in 3 feet of water and the upstairs occupied by residents, with lights and air conditioning running, whilst the sockets on the first floor were obviously in the soup. That was because the buildings were built for that, with the pole line, meter and service panel being on the 2nd floor, and the only wiring to the first floor being branches that were GFCI protected with GFCI devices that are upstairs (probably GFCI breakers). The GFCIs tripped, life went on.