I might be able to shed some light here. See, I generally DM in a way that generally appeals to players like your friend. I’m going to try and explain my reasoning and it might help you understand what he’s looking for.

In my games, the PCs generally succeed in their broad aims. We play to find out, not if they can, but how they do it, and what does it cost them. Character death is rare, and if I can help it, it’s never due to a single missed roll. Players get the opportunity to adjust their plans, sneak out when they are obviously outmatched, and are able to make miraculous escapes in the nick of time. When things go really wrong, are knocked unconscious and left for dead, or are captured. (If you are wondering how to run this, look at fate points in wfrp 2e, the idea is you give them a negative consequence and take them out of the fight instead of killing them outright).

This does not mean characters never die. A campaign that doesn’t end without a pc sacrificing themselves for the greater good is boring, but this makes it a conscious choice of the player.

This does not mean the PCs can just fail their way to success. They get plenty of opportunity to figure out a strategy that gives them the upper hand, to out-talk, out-plan, out-number or out-think foes too powerful to take on head on. But if they are dead set on doing it the stupid way, and I am satisfied I have provided enough information telegraphing the way it will end, then yeah, TPK away.

For me it's a question of balance.

Most smaller encounters are easy for my PCs, but major encounters should be tough, have a risk of PCs dying and also have the rewards be epic.

This is all just my opinion though, but seems my group likes it.

Adjusting the game to fit your table is the hardest challenge of all unfortunately. There are some players who don’t fit certain tables and DM styles and it’s your job to either make it work or tell them to find another table.

I think in your case you can make it work, but you’ve got a lot of work to do since you’re trying to accommodate a carebear happy fun time player at a table you want to run more and more as “hardcore-lite” experience.

I think two ideas I would have for you are to present your hardcore challenges as optional / non lethal challenges in a arena type colosseum. This lets you design difficult encounters but sandboxes them from consequences. If you want there to be consequences you’re going to make the carebear sad.

Another option is to come up with a McGuffin for the carebear that acts as protection for their character. E.g they fail there death saves and they turn into a rampaging monster due to some story reason. Lots of bad things happen to the party, but carebear wakes up the next day fine. You can use this to change the dynamic of “carebear” go frontline while we hit badguy. The big problem here is protecting the carebear leads to possible resentment from the other players so doing something like this is dangerous overall, but it can work depending on your players and how you do it.

For a TLDR I think you want to run more hard core games and your “carebear” player no longer fits at the table you want to run. In short you have to accommodate the “carebear”, change their mindset, or create a table of people ok with a more hardcore game.

You said in another comment that you enjoy DMing a game that has unpredictable results for the DM as well. A lot of good advice has already been given, but might I suggest giving your players more agency that you'd most likely see falling into the realm of the DM usually, so they create unexpected events for you as well?

Say you have the character of your friend destroy said Annis Hag, but blast! she had a curse prepared to fall upon anyone who would dare defy her to the point of death. Now instead of throwing your idea of a punishing burden on the player, you could instead go: "You can feel an evil magic engulfing your very being. It muddles your senses and try as you might, you are incapable of escaping its grasp. As it burns itself into your very bones and soul, you feel one of your abilities weaken. Which ability is affected?"

That way the player retains agency, can pick the least punishing option (in their opinion), have consequences but it doesn't feel like they just got punished for doing well or making a choice just as much as you simply deciding "That's how it is now. Enjoy!". Could also add an element of chance and put it down to a roll of the dice, but that might again feel too arbitrarily punishing to that character.

The curse then mightn't just have that main effect, mind you. But at least the worst one is more down to what the character feels and fears rather than what the DM wants to dish out. It will also give you something to ponder and think about in how to work with whatever the player chose or came up with. You could let them describe how the curse alters their appearance, do they suddenly have a mark on their skin? If so where, what size, shape and color? Now you have a PC with an odd mark of their own imagination and you can build on that. Or the player might come up with horns sprouting from their head, etc. Using this, you can have NPCs react to these changes and really play into them.

Player Agency might help alleviate the feeling of it being a punishing campaign, by giving them some room to breathe in all the pressure and stress.

I'm a newer DM who started a campaign 3 years ago during COVID with my brothers. Take my advice with a grain of salt because it may be different from others. My campaign is based around a group of characters that go from start to finish. My campaign revolves around some star wars fanfic I wrote back when I was too poor for college classes, yet knew my writing needed work. Thus, as a DM, I'm the one unwilling to allow player character death.

I am extremely lucky to have very mature players that mostly don't try to cheese the game. I usually give them a time limit for a mission to be completed, either explicitly from the quest giver, or implicitly where "bad things" will start to happen the longer time goes on and the mission isn't completed.

Could my players take more long rests? Absolutely, but that could cause them to fail that quest. Could my players take a long rest in the middle of the day right after waking up that morning? Absolutely, but they better have a plan for what they are going to be doing that night when all the shops are closed, it's dark, and NPCs want to be left alone. And besides, it's tough to fall asleep once your circadian rhythm is off... It would be a shame if characters needed to start rolling constitution checks to see if they can fall asleep to get that long rest for the next couple of days, and imposing exhaustion levels for not getting a long rest if it goes on long enough...

You're NTA, but your friend is also NTA in my opinion. There is a lot of communication that needs to happen here and they also need to be able to trust that you're not "trying to kill them". You, as the DM are trying to tell their story in such a way that they feel epic, yet balance that by in-game consequences. It might be a good idea to try and sprinkle in some consequences for constantly resting, like the insomnia/circadian rhythm mentioned above, or maybe an ambush from bad guys that figure out the heroes location and prevent a long rest from happening. Forcing them to flee and hide after the ambush, wasting the rest of the day, might help them get moving. Those ambushes should be scary enough that they would go to great lengths to avoid a repeat.

And one final thought is to possibly think of your campaign like a movie. Yes, you're telling their story, but you're not telling every moment of their story. You're not forcing their characters to stop for 3 meals a day, go to the bathroom, and occasionally wash their clothes and take baths. No, you're hitting the important parts of the story, and filling the gaps with downtime where they can fabricate things, work "jobs", etc,.

I hope something I've rambled about helps you out!

It kind of sounds like your friend won't enjoy the kind of D&D you like to run, and that's okay. You are allowed to enjoy running a challenging campaign with metered resources and meaningful stakes, and he is allowed to enjoy playing a shining hero that doesn't worry about restraints and desperate measures. Both of those games are perfectly fine as long as everyone is having a good time.