You had a question regarding audio extraction in the General Discussions for The Master Chief Collection, but that appears to have been deleted (If you didn't do that yourself, then perhaps it was due to the contents of my response), so I'll try again here instead:

I've got old extractions from the .MAP files of the Xbox 360 games performed via 'Adjutant[forum.halomaps.org] (v4.0.0.0)' available that contain a certain amount of the relevant files, but these are rather old, have some missing data mostly due to the tool's limitations at the time (Although I recently discovered that I clumsily missed the correct 'Coastal Highway' .MAP file for Halo 3: ODST) and otherwise need a proper revisit. There are others for Halo: Combat Evolved (PC-CD) & some mods that I did via 'Refinery' as part of the MEK Essentials[haloce3.com], but these need some catching up on and the Halo 2 (PC-DVD/Vista) is both notably lacking in certain areas & has low quality audio (Support for that game from 'Refinery' was incomplete). Nevertheless, these should include some of what you are after, which should be the "Foley" for the Halo: Reach Sniper Rifle and the Gauss Hog "Fire" audio from Halo 3, Halo 3: ODST & Halo: Reach (Possibly even Halo 4 if 'Adjutant' was able to extract that from it's limited pool of audio that it could). However, I am recognising Battlefield 4 audio being used for the Bigass V3 weapon in question (At least the Magazine Eject & Insert are definitely from the M82A3 as featured in the game), so extracting what you want from the mod itself may perhaps be the best way to go.

What I believe your best present-day solution would be, especially to use with The Master Chief Collection, would be the successor to 'Adjutant', 'Reclaimer[github.com]', which should have much stronger audio extraction support and should now even include the ability to access & export audio from the .MAP files for Halo 2 (Xbox) and perhaps whatever .MAP files used by community mods for The Master Chief Collection as well.

'Refinery' could still be a go-to for Halo: Custom Edition & mods (It's what I used for The Silent Cartographer: Evolved & SPV3 (Part One) at the time), but it's been a few years since I was doing this and there might've been changes in this regard since then (You can download the Source Releases for The Silent Cartographer: Evolved[tsce.info] for one thing, something that Bigass V3 does make use of), so it's worth seeing what & how much 'Reclaimer' can support at present.
I do also have a "HMT.v3.ReleaseCandidate (HaloMapTools.exe)" on hand, but this might be one of the oldest tools I have on hand (I think I last used it over 9 years ago, with it likely being far older than that), so it may not be worth recommending for this particular task (Assuming if it can even still be acquired).

If you end up requiring access to CE3's archive of the .MAP files from the Xbox 360 games as well as Halo: Combat Evolved (PC-CD) & Halo 2 (Xbox), they can be found here[haloce3.com].


THE SHORT VERSION
There are possibly-still-viable options, but using 'Reclaimer[github.com]' with The Master Chief Collection is probably the best one to try first.