People as threats
You can keep monsters as monsters, but also include people as threats. People can be "talked to" but that doesn't mean they're reasonable. But what is fun and interesting about people is they can be cunning - they can adapt, and they open up a LOT of possibilities other than "fight to the death". I have a Big List of Combat Stakes which you can use to base these on.
This can still work in a world with monsters - as many monster stories end up showing - people still have rivalries, greed, and ambition - and they may end up trying to engineer ways to get other people screwed over BY USING the monsters to their advantage (or, imagining they can, which then turns around and screws everyone...)
You can't reason with a tiger, but a tiger is not a "monster" in a supernatural sense. A tiger will try to hunt, and if it looks like too much of a problem, if the prey fights back too much, it'll run.
There's a lot of D&D style monsters which are basically trumped up predators (Owlbear, Bulette, Wyvern, etc.). Have them act like a predator - they attack by surprise, try to grab the weakest, most tasty looking victim and run off. Sometimes they make display threats to protect their territory or their young.
This, too, shifts the profile of a "win scenario" - driving off the creature or simply not having it provoked into attacking before you can get away are a win case too. It also means characters with the appropriate Knowledge skills can read what's going on and come up with alternative solutions.
More than what the sword can do
In horror movies, the monster often can only be defeated by doing something specific - you need to close the gate, you need to find the sigil, you need to put the two jewels together, etc. etc. When you make monsters set up like this, and the players know that their weapons will not really avail them, they have to consider fighting defensively and focusing on the goal.
You can also set up situations like the horde of monsters and things like gates that need to be closed. "You have to close the gate in 12 rounds or they WILL over run the town." "You need to get OUT of the woods, once you're out of the woods, they have no power upon you..."
These obviously are more contrived, but they also make more sense than simply having to fight everything down to zero HP.
A key point is to give players XP for however they defeat the monster - show them that beating everything down isn't the only way to get success.