Saving PNGs withous color profile embedded

If you are re-opening back into Photoshop to test, check your Preferences > File Handling > Ignore EXIF Profile Tag, which would need to be ticked/active to stop Photoshop automatically assigning the sRGB profile:

Using independent software to verify if a profile is embedded is often a good move.

Why do you think the profile is still embedded? Where are you seeing that?

Dave

Perhaps try a thorough reset of Photoshop preferences?

(read this entire post before acting please)

Resetting restores Photoshop's internal preferences, which are saved when Photoshop closes.

If they become corrupt then various issues can occur.

Here’s some info on how to do that:

https://helpx.adobe.com/photoshop/using/preferences.html

Manually removing preferences files is the most complete method for restoring Photoshop to its default state: 

https://helpx.adobe.com/photoshop/using/preferences.html#Manually

Manually removing preferences files is the most complete method for restoring Photoshop to its default state. This method ensures all preferences and any user presets which may be causing a problem are not loaded.

1. Quit Photoshop.
   
   
2. Navigate to Photoshop's Preferences folder.
   macOS: Users/[user name]/Library/Preferences/Adobe Photoshop [version] Settings
   Windows: Users/[user name]/AppData/Roaming/Adobe/Adobe Photoshop [version]/Adobe Photoshop [version] Settings
   
    
   Note: The user Library folder is hidden by default on macOS. To access files in the hidden user Library folder, see How to access hidden user library files.
3. Drag the entire Adobe Photoshop [Version] Settings folder to the desktop or somewhere safe for a back-up of your settings
   
   
4. Open Photoshop.
   
    New preferences files will be created in their original location.
   

Note re macOS: The user Library folder is hidden by default.

To access files in the hidden user Library folder, see here for how to access hidden user library files.

https://helpx.adobe.com/x-productkb/global/access-hidden-user-library-files.html

Unexpected behaviour may indicate damaged preferences. Restoring preferences to their default settings is a good idea when trying to troubleshoot unexpected behaviours in Photoshop. check out the video

https://helpx.adobe.com/photoshop/using/preferences.html#reset_preferences

Learn how to access and modify Photoshop preferences and customise per your frequent workflows

https://helpx.adobe.com/photoshop/using/preferences.html

And here’s an earlier forum discussion as an aid to understanding

https://community.adobe.com/t5/photoshop-ecosystem-discussions/quick-tips-how-to-reset-photoshop-preferences/td-p/12502668

You may want to backup your settings and custom presets, brushes & actions before restoring Photoshop's preferences.

Here is general info about that:  https://helpx.adobe.com/photoshop/using/preferences.html#BackupPhotoshoppreferences

Before you reset your preferences

in case of future issues, I suggest you make a copy as Adobe may need one to check problematic references. 

Quit Photoshop.
Go to Photoshop's Preferences folder

Preferences file locations: https://helpx.adobe.com/photoshop/kb/preference-file-names-locations-photoshop.html\

  [on MacOS see: Users/[user name]/Library/Preferences/Adobe Photoshop [version] Settings

  Note for those on macOS: - be aware that the user Library folder is hidden by default on macOS.

  https://helpx.adobe.com/x-productkb/global/access-hidden-user-library-files.html

  In the Finder, open the “Go” menu whilst holding down the Option (Alt) key.

  Library will now appear in the list - below the current user's “home” directory. ]

Now you can drag the entire Adobe Photoshop [Version] Settings folder to the desktop or somewhere safe as a back-up of your settings.

Note for those on macOS:

Preference preservation is affected by macOS permissions,

you’ll need to allow Photoshop ‘Full Disk Access’ in your Mac OS Preferences/Security and Privacy

If that doesn't fix the issue:

Go to Preferences > Performance... and uncheck Multithreaded Compositing - and restart Photoshop.

Still hanging? 

Go to Preferences > Performance... click Advanced Settings... and uncheck "GPU Compositing" - then restart Photoshop. 

Do you still have problems?

It may even be time to reinstall Photoshop.

It’s recommended that you use the Adobe CC cleaner tool to remove all traces first.

(See above about preserving preferences though! It’s worth preserving them unless they are corrupted.)

https://helpx.adobe.com/creative-cloud/kb/cc-cleaner-tool-installation-problems.html

Uninstall Photoshop BUT make sure to choose the option “Yes, remove app preference”.

Once that process finishes, start the installation process and look into the “Advanced Options”. Uncheck “Import previous settings and preferences” and choose to “Remove old versions”.

I hope this helps

neil barstow, colourmanagement net :: adobe forum volunteer

google me "neil barstow colourmanagement" for lots of free articles on colour management

Why do you think it has a color profile - what are you viewing it in? PNG handles things much differently than jpg.

How PNG handles color from wikipedia:

PNG supports palette-based images (with palettes of 24-bit RGB or 32-bit RGBA colors), grayscale images (with or without an alpha channel for transparency), and full-color non-palette-based RGB or RGBA images. The PNG working group designed the format for transferring images on the Internet, not for professional-quality print graphics; therefore, non-RGB color spaces such as CMYK are not supported. A PNG file contains a single image in an extensible structure of chunks, encoding the basic pixels and other information such as textual comments and integrity checks documented in RFC 2083.^[7]

I cannot reproduce the issie with File > Save a Copy, how exactly are you saving the png?