I'm not a huge fan of giant walls of text, so I'll post my breakdown behind a hidden collapsible section:
Argument 1: Possible Uses of Six Paths Abilities
Deva Path
In chapter 685, Kaguya uses what at first glance appears to be the Almighty Push technique which is accessible through the Deva Path.
However the actual technique she used is not named, and there is a very clear alternative that it could be.
Response 1: Eighty Gods Vacuum Attack
Supporters of her using the Almighty Push states that her stance is the same as a user of the Almighty Push would do; aiming her hand outward at her targets, however this is also the same stance she took when using the Eighty Gods Vacuum Attack.
Additionally in the anime version of this scene which expands on what we're shown in the manga (which is just the single page), we see
that Kaguya uses the Eighty Gods Vacuum Attack, and not the Almighty Push at any point.
Response 2: Lack of Usage Elsewhere
If Kaguya really was capable of using the Deva Path in this way to push her opponents back... why did it not even cross her mind when she was surrounded by Naruto and Sasuke later?
It's one thing for characters to forget their abilities but Kaguya has all the time in the world to think things through and we do actually see her considering her options. If she had an omnidirectional gravity wave capable of repelling her opponents, then it would have crossed her mind.
Preta Path
In chapter 682, Black Zetsu states that Kaguya can absorb 'any and all jutsu' and she seemingly demonstrates this later in the chapter by apparently absorbing Sasuke's Amaterasu.
Black Zetsu does not state that this is due to the Preta Path's ability and I have reason to think that it is not:
Response 1: Visual Differences
In the majority of cases whenever a user of the Preta Path absorbs a jutsu their body is surrounded by a noticeable effect as they draw the jutsu in to themselves.
Examples can be seen here, here and here.
Kaguya has no such aura around her. Instead the Amaterasu appears to simply disappear.
It is entirely possible that whatever allows her to absorb incoming jutsu is an entirely different method to the Preta Path. Since, after all, it is not stated that the Preta Path is the only method of absorbing Ninjutsu.
Response 2: Black Zetsu
When Kaguya has paralyzed both Naruto and Sasuke, instead of touching them directly, she uses Black Zetsu as a medium to absorb their chakra.
Users of the Preta Path can absorb chakra with direct contact; yet Kaguya notably does not.
Absorbing chakra is not a unique trait to the Preta Path in the series either, lots of characters have displayed this ability. So even if Kaguya could absorb their chakra directly herself, it is not conclusive proof of her using the Preta Path.
Argument 2: Sasuke's Statement
In chapter 678, Sasuke refers to the Infinite Tskuyomi as 'Rinnegan Genjutsu'. This of course carries the implication that if the Rinnegan is used to cast the Genjutsu then the user has the Rinnegan.
Response 1: Lack of Objectivity
To be clear, Sasuke is not an objective authority for information. He is uncertain about whether the Genjutsu can even be cancelled out by his Rinnegan, and he has never heard of the term 'Rinne Sharingan' in his life. He wouldn't know the proper terminology for it.
If anything, Sasuke called it 'Rinnegan Genjutsu' because he only knew that Madara had the Rinnegan for his eyes already.
Response 2: Hagoromo's Statement
In chapter 671, Hagoromo states that his mother wielded the power of the
Sharinga in order to put the populace under a Genjutsu.
Hagoromo is a more trustworthy source of information from Sasuke on this, especially in regards to Kaguya.
Response 3: Hagoromo's Statement Cont.
Earlier in that very page, Hagoromo states that Madara is attempting to come close to his mother's power. By this point Madara has already became the host for the Ten-Tails.
The only way he could come closer to her is if he actually awakened the Rinne Sharingan (something which she has that he does not) which he later had to do in order to activate the Infinite Tsukuyomi.
If the Infinite Tsukuyomi was a pure Rinnegan technique, then the user should not need to awaken the Rinne Sharingan before activating it.
Conclusion
In my responses to the first argument, I have demonstrated how it is not only plausible but likely that Kaguya has not actually displayed any of the Six Paths techniques in the series at all.
In my responses to the second argument, I believe I have outlined exactly why we should not consider the Infinite Tsukuyomi to be a pure Rinnegan technique and therefore why its usage does not imply the ability to use the Six Paths techniques either.
As a side note, we also don't treat the Ten-Tails as possessing the Six Paths techniques despite also possessing the Rinne Sharingan.