Currently have a 9mm upper with about a 7.5 inch barrel and has worked flawlessly.

Looking to go shorter in length.
What is the general consensus on shortest barrel length for 9mm upper and still function?
Where is the sweet spot since 9mm doesn't have any adjustable gas block to play with?
Would be used with various bullets (115, 124 and 147gr bullets) and sub-sonic loads and at times with a suppressor.

Searching and found optimum lengths ranging from 3-7 inches.
Its seems to be more of a range than a specific length.

My 9mm upper sports a 4.5” barrel.  It shoots anything quite accurately including 147s with a suppressor.

I think the available handguards are going to have more to dictate barrel length.  For function, there isn't much limitation.  Too short and you need to be wary of your fingers

I went with 8" plus a KAK can because I wanted to fit in a 10" handguard.

Things to consider:

Within limits, velocity will increase with each additional inch of barrel length.  Optimal velocity "efficiency" is around 8-10".  You get severely diminished returns on every additional inch beyond that.

Most defensive pistol bullet designs are optimized for the velocity from of a 4-5" barrel.  More length=more velocity=overexpansion and reduced performance. At the other end of things, too short of a barrel may cause the bullet to underperform.

For suppressor use, most 147s will remain subsonic out of traditional pistol-length barrels (3.5"-5.5").  Longer barrels may send them supersonic, reducing suppressor performance. Shorter barrels (3.5") may keep borderline supersonic 147s subsonic.

My two builds are 4.5" and 5.5", use 11 oz. buffers, and work great with a suppressor. All the 147s I've used so far remain subsonic.  

Recommend a hand guard 1.25" - 1.5" shorter than the barrel if you want the barrel threads and mating shoulder fully exposed outside the end of the hand guard.  I have 4" hand guards on both and I needed a 0.7" barrel extension to use a suppressor on my 4.5" barrel.

I like 7-9".  
Of course the speed of sound will vary depending on density of the air, temperature, altitude etc...
I'm in Florida and I reload.
I reload 99% of the time 147Gr JRN.  I also use Titegroup.  Max charge is 3.6Gr.  I load to 3.7.  Even at a tad over max charge, it is still subsonic out of a 10" UZI SMG barrel.
Now as previously stated self defense HP ammo would be supersonic out of this barrel length which I can confirm is true....but I'm not dumping a bunch of HST, Gold Dots downrange.....on that note, I think every FACTORY JRN 147 Gr is has still been subsonic for me out of a full size UZI SMG....the exception to that is the old FNM 147 Gr that stuff was really hot and would go supersonic on me.  Not sure if that is even available anymore...I'm sure there are more
exceptions.

Another thing to note is that the shorter the barrel the more the suppressor has to work.   Tom Bowers posted on Subguns.com that he thought the 5" CMMG RDB was loud to him.  He stated he had not heard the 8".  I think my 8" CMMG RDB is really quiet and would put it on par with my suppressed MP5.

More powder is burned up in a longer barrel but this comes down to what powder you are using.
As mentioned, I'm using Titegroup which is pretty fast burning and I'm still not going supersonic even going over the Max charge...which BTW, I've tested up to 4.0Gr and then I'm going a little over 1000 FPS out of a 10" barrel.

I also like having more rail space which is why I like around the 8" or so range.  
I know you could get a rail that goes over the suppressor but I also like to shoot unsuppressed too....and I personally don't like my hand being in front of the muzzle when unsuppressed.

If you are using a suppressor and want the OAL short maybe 4-5 inches?
Once you get down to sub 5 inches what is the advantage of a 9mm upper?

There isn't a consensus.

Depends on how you will use it.

16" - because you never know what the ATFE is gonna do.

9mm Luger Results in fps