I haven't seem Time Tunnel, so I cannot comment there.
Quantum Leap is not a show where the time travel itself is the plot. The time travel is a setting in which to have episodic adventures - what you did in the last location does not impact the present location, and that will not impact the next. There is tension arising from the local situation, but not from how this period connects to others. As you say, it is like Sliders - alternate reality jumping. Time travel as setting, rather than plot.
This, as compared to, say, Timeless, where the impact of the past on the present and future really is the point, and strongly drives the character's need to act, and what decisions they make.
Actually, if one follows the whole series, yes, the actions in the various times are a singular metaplot - each little correction is needed before we can see the protagonist return home. It's very similar in basic concept to
Voyagers... except that
Voyagers has actual time wars referenced, while it's merely implied in
Quantum Leap. We always know Sam has to figure out what's wrong, and then make it right, so he progresses onward. Likewise, Phineas and Jeffery have to figure out what's wrong, fix it, and move on... without Phineas' cheat book.
This gives the two a somewhat different feel, as we don't know (until the final episode) what Sam's been fixing.
Meanwhile, Voyagers is a more open conflict, much like the more recent Legends
of Tomorrow. And LoT is even more blatant, in that they're actually pursuing inidividuals who are intentionally messing up the somewhat elastic limited multiverse timelines. (DC has at least 3 universes in the TV lineup... One has Both the Supes, one has Flash, Arrow, and a number of others, including the core of LoT, and then the Gotham Verse....)
In all three, the core conceit is history needs to be nudged back into shape, and the protagonists travel isn't entirely their choice nor entirely under their control. But it is the matrix in which their adventures happen. Essentially, they're timecop stories.
Not having seen Timeless, I can't speak to it..
I can say that if I were going to be doing a time travel campaign, timecop mode allows for the best balance of "Here's a situation, now go fix it." Quite literally, it makes the time travel the narrative framing, and the corrections can be provided via hints on the timeship... ala
Legends of Tomorrow.