Andy,
I hope all is well. There are two ways to go here, depending on what system you are looking at setting / modifying SIP addresses for.
If it is Lync / Skype for Business, then the following is what you would need:
https://docs.microsoft.com/en-us/powershell/module/skype/Set-CsUser?view=skype-ps
If it is for Exchange (on-prem, or EOL), then you would actually use the syntax Ronnie has indicated, but there is a slight "twist" or issue to be aware of so that the Syntax is set correctly.
https://docs.microsoft.com/en-us/powershell/module/exchange/mailboxes/set-mailbox?view=exchange-ps
Read the -EmailAddresses parameter section, approx. 1/2 way down page, as reproduced below: Specifically, you want the very last part at the bottom, as shown below:
To add or remove specify proxy addresses without affecting other existing values, use the following syntax: @{Add="<Type>:<emailaddress1>","<Type>:<emailaddress2>",...; Remove="<Type>:<emailaddress2>","<Type>:<emailaddress2>",...}.
This may be the confusion, as it looks like the syntax you are referencing above is not 100% correct.
Also, using the -WindowsEmailAddress parameter can have unexpected results, as noted:
Using the WindowsEmailAddress parameter on a recipient has one of the following results:
In environments where the recipient is subject to email address policies (the EmailAddressPolicyEnabled property is set to the value True for the recipient), the WindowsEmailAddress parameter has no effect on the WindowsEmailAddress property or the primary email address value.
In environments where the recipient isn't subject to email address policies (the EmailAddressPolicyEnabled property is set to the value False for the recipient), the WindowsEmailAddress parameter updates the WindowsEmailAddress property and the primary email address to the same value.
The WindowsEmailAddress property is visible for the recipient in Active Directory Users and Computers in the E-mail attribute. The attribute common name is E-mail-Addresses, and the Ldap-Display-Name is mail. If you modify this attribute in Active Directory, the recipient's primary email address is not updated to the same value.