Changing what the length of time is for a "rest" just to tweak healing will have TONS of unintended side effects.
Let's go with that gritty thing for example where a short rest is 8 hours and a long rest is a week.
Dragonborn Breathweapon usable once per day.
Half Orc - Relentless Endurance once per week.
Barbarian - Rage uses only recharge after a week, and Relentless Rage doesn't reset it's DC until the next day.
Bard - Expended Spell slots & Bardic Inspiration regained only after a week. Font of Inspiration becomes a daily.
Cleric - Expended spell slots regained after a week. Channel Divinity is once a day. Divine Intervention takes a week before you can use it again, whether you succeeded or not.
Druid - Expended spell slots regained after a week. Wild Shape only recharges the next day.
Fighter - Second Wind & Action Surge both become once per day. Indomitable takes a week to recharge.
Monk - Ki recharges only after a day.
Paladin - Divine Sense & Lay On Hands, Cleansing Touch, and Expended spell slots only recharge after a week. Channel Divinity takes a day.
Ranger - Expended spell slots take a week to recharge.
Rogue - Stroke of Luck becomes a daily.
Sorcerer - Expended spell slots and Sorcery Points take a week to recharge.
Warlock - Expended Spell Slots & Mystic Arcanum & Eldritch Master recharge after a week.
Wizard - Expended spell slots regained after a week.
Now that was only with the base races and classes, though some specialties/traditions/whatever that class calls it have more things that get screwed over. If you want a really low magic and special ability campaign, that almost works, except there are plenty of amazing things some classes or races can do who's recharge times are not based on "rests" which get distinctly MORE powerful in that kind of setting.
If you want to change healing rates, do NOT redefine the lengths of "rests". Instead, just move healing off of the "rests" system and give them times (hours, days, etc). Doing it like that, you'll avoid screwing up everything else.