"Error code 121: Error writing to the temporary file location
"Error code 121 indicates that the installer has issues with the temp folder settings or access to them on your device.
"Solution
"Fix permissions for the temporary location. Then, try to install the app again."
I'll move your post from Photoshop to Download and Install. Please give your macOS version and whether or not your computer meets the system requirements.
https://helpx.adobe.com/photoshop/system-requirements.html
Recent versions of macOS require giving accessibility permission and sometimes users automatically say no when they should say yes. This article from MacWorld may help.
https://www.macworld.com/article/347452/how-to-fix-macos-accessibility-permission-when-an-app-cant-be-enabled.html
You can also try these:
https://support.apple.com/guide/mac-help/change-permissions-for-files-folders-or-disks-mchlp1203/mac
https://support.apple.com/guide/mac-help/if-you-need-permission-to-open-an-item-on-mac-mchlp1038/mac
You can also try running Disk Utility to repair permissions. Find it with Spotlight if you haven't used it before.
If these links don't work and no one on the Download and Install forum has additional ideas, then contact Adobe Customer Care:
https://community.adobe.com/t5/creative-cloud-services/how-to-contact-adobe-support/td-p/11875703 (type "agent")
or send a tweet to @AdobeCare for support.
Don't respond to PMs, as they may be scammers.
Let us know when and how you succeed!
~ Jane