No, there is no evaluation edition of Standard Edition, only of Enterprise Edition.
To move from Standard to Enterprise, you don't need to reinstall, but you run an edition upgrade. Thus, there will be a bit of downtime, but everything is done in place.
For more details on the edition-change scenarios see this page: https://learn.microsoft.com/en-us/sql/database-engine/install-windows/supported-version-and-edition-upgrades-2022?view=sql-server-ver16.