I come from 3E and, while still very combat heavy, this edition supported "other" parts of the game by having out of combat skills and spells which ,instead of being improved (which would have been necessary) were completely missing..
There's a distinction between non-combat and non-adventuring. You don't normally pick a lock in combat, for instance, but you may do so quite often while exploring a dungeon. You don't normally make jewelry or bake a cake in combat, and you're also pretty unlikely to do either while exploring a dungeon.
AD&D had 'secondary skills' that could be distinctly non-adventuring (like cooper), and 3.5 had several open-ended skill groups that could be used to devote precious ranks to non-adventuring skills. 5e seems likely to continue that tradition, since skills seem to be prettymuch wide-open. If your background is 'blacksmith,' for instance, I'm sure you'll have a +3 to making horse shoes and so forth.
how much of the next edition will be devoted to non combat interactions?
It remains to be seen, of course, but given the modular approach, you have to expect there will at least be extensive optional rules for baking or macrame or ferret juggling or whatever it is you want to do when you're not adventuring...
One thing I noticed is that, functionally, by the numbers, the 5e skill system and 4e skill system are very similar. Anyone can attempt to use any skill and being 'trained' only gives you a static bonus. The difference is the 4e advancement treadmill vs 5e non-advancement, and that difference is pretty minimal, mathematically. In 4e, if your trained in a skill, you have a +5 and if you have a very high stat you're +4 or 5 or so, depending on level. In 5e, if you have a good stat, you're +3 or so, and if you're trained you're +3. In 5e, if you go up in level, you don't get any better; in 4e, if you go up in level, you don't get any better relative to a level-appropriate challenge.
The big difference is that 4e uses a finite skill list and 5e doesn't. So, in 4e, if you want a character who's a good diplomat, you look at the skill list and take high CHA and training in the skills that seem most applicable - like Diplomacy and Insight. In 5e, you'd want high CHA, and then you'd try to pick a theme that gave you a +3 in diplomaticky situations - like Diplomacy and Insight and Heraldric Lore and Politics and Conversation and Etiquette and Dance: Pavane and whatever else you might think of or your DM might call for. You could spend a whole adventuring career collecting +3 diplomatish bonuses and still find yourself without a +3 in one diplomatic incident after another. You don't have "Hobgoblin Tea Ceremony?" ooh, you're at a Disadvantage for this negotiation...
That's the thing about open-ended skill systems, they create incompetence each time you add a new skill.