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.
Hopefully they’ve come a long way since this talk, but hearing about the situation in 2016 I’m not surprised: https://youtu.be/7KXVox0-7lU?si=fHaxSKvw5MIlg__2