Does Microsoft provide paid support for SQL Express?
I can't find any great documentation to back this up other than articles referring to SQL Server 2005 like this one here.

I also just tried to create a ticket for SQL Server Express, and the support site lists Express as an option. You can see for yourself by starting here. I've chosen support, developer or IT support, SQL Server, then SQL Server 2016 and finally the option for edition came up and I chose Express.

Microsoft provides support to customers of SQL Server express in the same manner as SQL Server Standard and Enterprise - if you have a support agreement with hours or pay for hours, you'll receive support. If an item is found to be a bug in the product, typically the case hours or money are refunded/not applied, if it is user error/application issue on your end/etc the hours are used like normal. SQL Server licenses of the paid versions don't automatically give you access to support. Support is a separate offering, effectively.