The difference between long rests and extended rests is very intentional. Extended rests often mark the end of an adventure, or at least reaching a place that is totally safe. It certainly should be a goal for players to do so and it is very strong limiting factor in preventing Ruins of Symbaroum characters from being 'fantasy superheroes' that a very generous interpretation of the regular 5e rules would encourage.
We do have a variety of mechanisms for getting some Hit Dice back or mitigating/helping their use:
Overall
Everyone always gets the equivalent of using one HD (with the maximum value showing) every long rest. You always heal a little bit.
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Captain
- Field Dressings - Extra 1d6/1d8/1d10/1d12 hp when you also use a HD
War Stories - Restore X HD (where X=your proficiency bonus) to everyone you share a rest with. 1/2 times per extended rest
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Mystic
- some approaches can cast healing spells
Natural Alchemy - in a wild place, generate X tonics (where X=proficiency bonus) once per long rest. Each tonic restores 1 HD.
Symbolists can regenerate hp, avoiding the need to spend HD for hp (how good a deal this is depends on level and other sources of Corruption)
Medicus (Theurg) - restore double X HD per extended rest / restore double X (HD + 1d8 + Wis mod), so the affected creature essential gets the effect of the HD immediately and gets to keep the HD to use in any way they wish.
Nature's Bounty (Witch) - can make Alchemical Elixirs in the wild.
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Scoundrel
- Channeling (Former Cultist) - you could select spells that provide healing
Firetube (Sapper). - this gives you proficiency with alchemist's supplies, more about being able to make your own ammunition, but can be used for Elixirs as well.
Alchemical Expert (Sapper) - this is a late game feature more to do with keeping yourself supplied with ammunition, but can be used for Elixirs as well.
Alchemy (Treasure Hunter) - this can allow the character to make Elixirs, such as Herbal Cure, which can help mitigate the need to spend HD.
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Warrior
- Battle Wind - these temporary hit points can prevent the need to spend a HD on healing.
Medicus (Templar) - qualify for the base version of Medicus.
Rage (Berserker) - resistance to common damage types reduces HD usage.
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Feats
- Robust (Troll) - damage reduction makes trolls less likely to need more HD, preferably freeing up them for other members of the party.
Ravenous Hunger (Undead) - allows undead to keep themselves at a minimum threshold without spending HD.
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So there's a variety of things — we want folks to sometimes get HD back, but we want it to be something special. Natural Alchemy itself is a matter of Gamemaster interpretation. It certainly doesn't work if the character is in an urban or cultivated environment. It probably doesn't work if they spend their whole day digging in the dirt at one location (no chance to gather the herbs or treat them). Compared to Medicus, it's going to be a matter of how many times the Self-taught Mage gets to use it, versus how many times Medicus can be used and at what level. And, of course, the Theurg has lots of other options for restoring hit points, whereas the Self-taught has a few less.