Beyond 4e's skill powers, there were also 4e's Martial Practices.
In 4th Edition, certain spells from earlier editions only existed as rituals, a separate mechanic for the type of magical spells that are not really designed for combat encounters and are bigger in scope. Alchemy recipes were introduced in "Adventurer's Vault" (an items & equipments-focused rules expansion); these functioned much like Rituals but with various alchemical ingredients needed and were more readily accessible than rituals for non-magical characters.
Then "Martial Power 2" introduced Martial Practices, which are like Rituals and Alchemy, only powered by healing surges (i.e. HD), and utilizing your skills, weapons and armor, and other non-magical abilities and equipment for non-combat functionality.
I believe that part of why we don't have these sorts of subsystems in 5e (at least, haven't had in 5e -- Circle Magic is reminiscent of 4e Rituals), was the pushback against so much defined subsystems in 3e and 4e.
I know in the circle is played 4E in, there was some issue with people thinking if it doesn't have rules for it, it's not legal to play and if you make up your own rules to cover do a cool stunt then the Fighter who took the exploit power to do that cool stunt now feels like a chump.
But Martial Practices were one of the coolest innovations of 4E, and I highly urge taking a look at them. Skill Powers are a bit smaller in scope but more specific on those skills, the problem is that the power system doesn't work very well with non-combat encounters bc the language and feel of these powers lend themselves to combat, and that influences the designers into trying to make the skill powers helpful for combat rather than like utility powers for exploration and social situations.
Martial Practices, by leaning into the explicitely non-combat systems of rituals and alchemy, were allowed to really explore what Martialists could do outside of their focus area.
If you're going to use them out of the box, you may need to change up some of the costs as HD are much less plentiful in 5E than Healing Surges were in 4E. I'd still lean into using Hit Dice, but I'd also let them use Superiority Dice, Action Points, Focus Points, rages, sneak attack dice, divine smites, hunter's marks, etc. I would NOT include Psi Dice in that allowance as those are explicitely psionic and not martial/mundane/physical in nature.