There are a lot of variables. If, for example the chasm is 25 feet and you have a 20 strength regardless of whether you have the movement to complete the jump.
I don't allow people to move further than their action economy allows in a single turn barring magic/special circumstances. Leaping further than normally allowed is certainly possible but a separate issue.
Oh and they don't "float" for a turn. From the PCs perspective their turns are happening one right after another, there's no time gap. We just can't resolve simultaneous in a pen-and-paper game. A single round takes the same amount of time if there's 1 creature acting or 50.
"Float for a turn" is not limited to "pc perspective".
But hey, kets look at the case of ending turn in mid air, allowing that to continue into next turn, and strict not allowing more movement than action economy.
During your turn in air... You get hit by any number of effects that mean you dont get movement nect turn.
Lets say psychic dmg renders you unconscious.
It doesnt move you, no physical impact...
Start of your next turn do you get free movement to compkete the jump even though you are uncobscious and unable yo move? Or do you plummet straight down?
Could be sleep spell or any number of other cases.
To me, it seems that one who is very concerned about the "pc perspective" rules framework might find it easier to minimize the whacky results by using the athletics jump rules to resolve the action.
It could even be a case of:
Make the check against dc x and get across with full move next turn.
Make it against dc y and make it across but lose some movement from bext turn.
Make it against dc z and make it across but (insert situationally appropriate effects)
Fail and dont make it across.
But to be clear as to where this can go, PHB defines failure on a check as "makes no progress towards the objective or makes progress with setback determined by the GM."
To me, it just seems a lot cleaner to use the options directly spelled out in the PHB to handle the edge case of "leaping over larger gap than current movement allows but which is within my normal leap distance" with skill checks and setbacks than to try and house rule in that hang-time that is not hang-time and all the exceptions it creates.
I think for many GMs, the check/resolve/setback would play out more quickly, fluidly and consustently to the base mechanics in a wider set of games than pseudo-hang time.
But, people love their house rules so, far be it from me to seek to change a more my rule sort of thing.