Your password is required to enable iCloud Photo Library. Open Apple ID in System Preferences to turn on iCloud Photo Library.

As per this article https://support.apple.com/en-in/HT211238

If upgrading from macOS Sierra or later, macOS Big Sur requires 35.5GB of available storage to upgrade. If upgrading from an earlier release, macOS Big Sur requires up to 44.5GB of available storage.

In your screen shot major of the space is consumed by documents , make sure you have turned on iCloud Drive and desktops and documents box is checked https://support.apple.com/en-in/guide/mac-help/mchle5a61431/10.14/mac/10.14

Delete the documents from finder https://support.apple.com/en-in/guide/mac-help/mchlp1093/10.14/mac/10.14

Also , only 6.06 GB is available out of 251GB and for upgrading Mac OS big sur minimum space is 35.5 GB

You have installed many third party applications in Mac , click on finder > applications , select the third party apps and move to bin , restart the Mac and empty the trash , this will increase Macintosh HD space , may be you are using 2TB iCloud storage space but that doesn't matter , the question is hard drive space so reduce it .

Also empty the trash , there must not be .dmg files inside it .

See some articles to reduce the data https://support.apple.com/en-in/HT204247

https://support.apple.com/en-in/guide/macbook-air/apdb468896e0/2019/mac/10.14.5

https://support.apple.com/en-in/HT206996

https://support.apple.com/en-in/guide/system-information/syspf5a64aa6/mac

For pop up of turn on icloud photo library see these articles https://support.apple.com/en-in/HT204264

https://support.apple.com/en-in/guide/photos/pht5156cc968/4.0/mac/10.14

Hello Phillymouse,

Thanks for using Apple Support Communities! We see you're getting an iCloud password prompt when trying to enable optimization for your Mac, and we'd like to help.

It does look like you've done everything correctly, as far as we can tell from your photos. Have you restarted your Mac since noticing this issue? If not, go ahead and do that, as a restart can resolve unexpected issues.

Log out, sleep, restart, or shut down your Mac

Then try again.

Optimize storage space on your Mac

If you're still getting the same error message, we'd suggest contacting Apple Support, and let them know what's happening.

Get Support

Take care!