What does "Bonus Quest Handin Progress" use for?

[77]

I got 7/9 by now, And found nothing changed.

[Fel]

The maximum is 8 across all of the features so I'm not sure what 7/9 represents.

Not that it changes how it works.
By default, no matter what the level of the quest item you hand in, it only counts as 1 for the quest.
The itopod perk 145 "Bonus Quest Handin Progress I" unlocks the ability to gain more from levelled items, specifically it gives 1+ level/10 (so 1 at level 0, 2 at level 10 and 11 at level 100).

All of the other "Bonus Quest Handin Progress" reduce the divider (the 10 in the formula above) by 1 per level.
There are 4 of such bonuses to grab (1 perk, 1 quirk, 1 evil wish and 1 sadistic wish), each has 2 levels for a total reduction of 8 with all of them at level 2.
What that means is that with all of them you are now gaining 1+ level/2 when handing in quest items, so a level 100 item would give 51 to the quest (essentially completing the quest unless you didn't reduce quests to 50 with the fibonacci perk).

This was added because a fairly frequent complain/suggestion was levelled quest items should not count for the same amount as level 0 ones.