Can I upgrade iCloud from my computer for my iphone13 as my iphone13 may not open, so I can backup all data photos etc on icloud that are on my phone to transfer over to new phone? Can this be done without opening my existing phone?

Yes. based on -> See this Apple article: Upgrade to iCloud+

Upgrade to iCloud+ - Apple Support

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scroll to -> Upgrade to iCloud+ on your Windows PC

1. Open iCloud for Windows.
2. Click Storage.
3. Click Change Storage Plan.
4. Choose a plan, then click Next.
5. Enter your Apple ID password, then click Buy.

See also the following Apple articles:

iCloud+ plans and pricing -> iCloud+ plans and pricing - Apple Support

How to back up your iPhone, iPad, and iPod touch

How to back up your iPhone, iPad, and iPod touch - Apple Support

If you still need help, get more help and assistant from Apple directly, see Contact Apple for support and service -> Contact Apple for support and service – Apple Support (UK) 

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as my iphone13 may not open

Do you have problem to open your iPhone 13?

And what do you mean with -> as my iphone13 may not open?