Sql-server – Export SSMS database connections to a new version

It sounds like your host has done the following:

REVOKE VIEW ANY DATABASE FROM public

...and this prevents browsing the database list in SSMS, although it doesn't stop you seeing that list using other techniques, or connecting to your database in a query window.

I think the only thing you can do is ask them to change it back, or at least to verify that that's indeed what they did.

In SQL Server Management Studio right-click your database and select Tasks / Generate Scripts. Follow the wizard and you'll get a script that recreates the data structure in the correct order according to foreign keys. On the wizard step titled "Set Scripting Options" choose "Advanced" and modify the "Types of data to script" option to "Schema and data"

TIP: In the final step select "Script to a New Query Window", it'll work much faster that way.