While I absolutely agree that this is the way to a game I tend to find enjoyable, I have to emphasize that it come with a load of non-obvious consequences.
Maybe the most obvious is that the players must be prepared to lose. This philosophy will lead to stakes players really dont want to fail go the wrong way. While many like this, my impression is that most prefer movies with happy endings when they are looking for pure fun entertainment. If your players just want to chill, relax and have fun, you either should to make sure there are never any real stakes on the table - or make sure the combats are winnable when those stakes come up.
The second is that you as a DM need to be prepared to see the players lose. You need to accept the pain of seeing all the player characters fall one after the other as they heroically try to save their downed team mates in a fight you had been telegraphed as hard as you could was a no brainer run away scenario. You have to accept your bellowed npc they were escorting being left behind for death when the characters teleport away from the encounter you knew would just be a walkover for them.
Several classic D&D issues like overly caution, not really caring about their characters and 5 minute adventuring day is becoming exponentially more probable unless you are very carefull and proficient in managing your game.
In short - what you are opening up is a very different kind of game than the "villian of the week" game where the characters prevents some bad stuff from happening, and get the feel good ending. You are almost forced onto a grim sandbox. If this is what you and your players want, then it is great! But you shouldn't introduce it expecting the result to be just villain of the week with increased tension.
Nobody loses when they create a good story. I find better stories emerge, at least with more open-world, sandboxy campaigns, when character death is on the table.
But I get your point. You need to be on the same page as your players. In my current campaign. We lean into it.
First, I asked if they wanted to play in a massive, sandboxy, very deadly mega-dungeon setting.
Second, the first session was a funnel of level-0 characters. Each player had 4 characters. The first encounter, and the only planned encounter in the 3+ year campaign was very deadly. They PCs were part of a large caravan, either paying "passengers/merchants" or those being paid to guard. It was carnage. Luckily there were lots of NPCs which helped most of the PCs survive due to a large number of targets.
Third, when we started the campaign, we were still playing in person. On the wall behind the DMs chair was a Obiturary list with lots of space for writing the names of the fallen and how they died.
Fourth, taking inspiration from The Glass Cannon Podcast's first campaign, I had a light-hearted adversarial DMing style in terms of comments I would make during combats, etc.
I don't have to telegraph encounters much, because expectations were set from the first session of play. It is up to the players to have their PCs to do the work to determine the level of threat an area or enemy may pose.
Yes, it resulted in a different style of campaign from my prior two 5e campaigns. But it is refreshing.
I don't believe that the players care less about their PCs. In fact, having characters that survive to high levels are more precious for having survived against the odds being stacked against them.
Yes, they have been a lot more careful, especially at low levels. The five-minute adventuring day really only seems to be a problem when you expect a certain number of combats per game or have a story-driven game that expects certain things to be accomplished in a given session. Combats are dangerous, draining experiences to be planned for and recuperated from. I don't see a problem with that. Whether they fight and retreat to safety to recuperate, or continue on, depends on where they are, who they are facing, and what their objectives are.
I find the fact that they can run into very deadly encounters greatly enhances the social and exploration pillars of play. Much more time is spent on planning, reconnaissance, gathering intel, research, creating networks, etc.
Turns out that the campaign has not turned out to be quite so deadly as advertised. With the 5e rules and veteran, strategic players, the PCs can prove quite resilient.
As they reached higher levels they can really enjoy being able to defeat enemies that were once quite terrifying. It creates a sense of accomplishment.