I like this example, because it shows the way it should work, assuming there are no interruptions. And for this circumstance, I'll say sure, what you describe makes sense. Implicitly, you've now told us how you understand one of the possible ways that might stop the jump being "immediately after" the run up: for you, the end of turn doesn't matter.
This isn't just a "for me" thing. This is how discrete turn modeling
works, in general, for everyone. The end of a turn, in and of itself, has no impact on the events that occur within the world.
Turns are a way that we can measure what's
actually happening within the game world, but how
we chose to measure those actions can't possibly affect
how those actions play out.
We don't exist, after all (as far as the game world is concerned). It's not like the natural laws of that world
actually change after someone draws a weapon; it's just that
we find it to be a more convenient model if we approximate the interaction of opposing forces in six-second increments rather than continuously.
What about (a) making an Attack action?
(b) Making an attack with a bonus action?
(c) Casting a spell?
(d) Making a reaction?
(e) Making a saving throw for half damage from a spell?
(f) Failing a saving throw for that matter?
(g) being attacked?
(h) taking damage?
The answer for almost every case is that it depends on the specifics. If you're running north at a constant speed, and you (a) turn to fire your bow at an enemy to the east, is that going to mess up your momentum? Probably not. It's easy enough to visualize the scene, and there's no need to stop in order to fire (although it's significantly easier to visualize if you're using a short bow rather than a long bow). If you are instead running north at a constant speed and want to (a) swing your maul at an enemy you pass by, then that's going to be a bit trickier.
Bonus action attacks (b) would, likewise, depend on what's going on. If you're some ninja rogue with two short swords, then you could probably stab an enemy twice without slowing down, because that's something a ninja could do. If you're a raging berserker, then probably not, because you have to put a lot of momentum into your swing.
Does (c) casting a spell require you to slow down while running? I don't see why it would. You're waving your arms and chanting, but unless fatigue starts to set in, there's no reason to assume that you're even breathing heavily. It's not like the standard jump rules make an assumption of perfect form. (The rules
are extremely generous in saying how far someone can jump, and how much room they need to get up to speed, but that's a separate matter.)
There are lots of types of reactions (d), so making a blanket rule for all of them would be ill-advised. As long as you're not running up to the edge and then delaying your action in order to jump across based on a certain trigger, I can't see why it would require
more effort than making an attack or casting a spell as an action.
Making a saving throw for half damage (e) usually means that there's a wave of fire washing over the area, as from a Fireball spell or a dragon's breath weapon. In either case, it doesn't apply a significant amount
force, so it's down to how you describe damage - which canonically varies from table to table. Did half of your skin get burned off? Then you're probably too distracted from the pain to continue running. The same goes for taking damage (h) in general. Was it a narrow miss which only burned away your luck and plot armor? Then you're fine and it doesn't interrupt your momentum.
If you fail a saving throw (f), would the effect that you were saving against alter your momentum? Are you paralyzed or sleeping now? Were you hit by a wave of force which pushed you back twenty feet (to the west, in this example)? If not, then you're probably still okay, barring the basic considerations of taking damage as described above.
If someone attacks you (g), what are you doing to defend yourself? If you're wearing heavy armor, and a giant is throwing a rock which bounces off of your armor, then that probably messed with your momentum. If you're in light armor, and someone is swinging at you, then there's no reason to assume that they either made contact or caused you to slow down, unless you used a reaction to parry or something.
Two points of further consideration:
1) The situations which I would argue against are also the ones which are less likely to actually come up during play. A rogue with a shortbow is much more likely to
want to fire while moving to jump across a gap, than a barbarian or paladin is likely to
want to run past a melee opponent.
2) The outcome of an action doesn't depend on whether or not you are "in combat" at the time. If your paladin in full plate armor is making a run to jump over a chasm, and a hidden giant (or pressure-based trap) throws a rock which bounces off of their armor, then that's going to interrupt the attempt equally whether or not you've called for initiative.