Zlib is usually corrupt files. Steam verify is known to have issues on some systems - other things can cause problems too - like antivirus/security software and permisions. If you are running 3rd party antivirus/security software - I would temp sleep/disable it - or add gtav folder to exclusions. I'd say check hdd space - but steam pre-allocates space and complains. I also vaguely remember some having issues with ram or malware/adware corruption.

Some things I would immediately do. Exit steam.
Open taskmanager and make sure no gtav/social club processes are running. (or restart pc)
Open steam / steamapps / downloading. If there is a 271590 folder or files - delete them.
Open steam / steamapps / temp - same thing. 271590 folder/files - delete them.
If you are installed to/using a steamlibrary - adjust the locations.
There should only be 1 appmanifest_271590--- the one ending in .acf.
If there are any appmanifest_271590. old, bak, tmp, etc - delete them.
Turn on filename extensions if necessary to doublecheck them.
You've already tried installing on a new hdd so that rules out the first one.

Next - I would drop in a current appmanifest file. The newest one is in this link -
https://gtm.steamproxy.vip/app/271590/discussions/0/276237094320417714/#c276237094320637525

After the appmanifest is put in (with steam closed) - rightclick steam - run steam as admin.
Verify cache once again. With the download/temp folders clean - it "shouldn't" have issues.

If you ever modded, verify the folder is clean too (better yet, verify it is clean.. anyways).
https://gtm.steamproxy.vip/app/271590/discussions/0/1499000547495596089/#c1499000547495630914

If you keep having problems - might have to eyeball the files, or get someone to crank out a md5 across the gtav/sub folders so you can compare - then delete the known corrupts (if any) and try again. (which shouldn't really be a problem - due to a new drive/install location)

Beyond that - I'd personally want to see it. New location rules out mods (unless unmentioned -.-). There are instances where windows updates have caused problems with gpu drivers but that hasn't created zlib errors in year+ to my recollection atleast.

edit - you could also try booting windows in safemode with network to fake a clean boot - and see if steam works / and will verify cache/download that way - not in mood to test that right now.

*zlib errors can also happen on some new drives with outdated firmware (typically, this immediately appears when you replace/change over to running off the hdd - not after a game update, etc).
They have also happened in the past due to a manipulated hosts file (cheating usually)

edit - 2023 - since things have changed over the years - - some additional info -
R*'s 'help/fixes' - https://support.rockstargames.com/articles/204775458/Failed-zlib-call-error-in-Grand-Theft-Auto-V-for-PC

And I have seen a few be due to temps, ram speeds/ xmp settings, and overclocks.
Adjust/test accordingly. Remove all test. Use defaults. Some things can also come overclocked (not always a good thing), and some things are 'auto' via the bios/other softwares. No, they do not always work perfectly. Test. Gta5 is notorious for working fine, and busting after various updates, and return fine after next update over the years in regards to overclocks.


Old thread -
https://gtm.steamproxy.vip/app/271590/discussions/0/1734342161850525010/#c1734342161850546223