Thankfully, code that runs on Developer Edition will also run on Standard Edition. There are very few surface-area feature which are Enterprise/Developer Edition only.
However, code may run in a different way from the point of view of performance, since some optimizer and performance features are not available in Standard Edition. This may be something you don't notice, but you can also be severely burned.
You can find a list of differences here: https://learn.microsoft.com/en-us/sql/sql-server/editions-and-components-of-sql-server-2019?view=sql-server-ver17, but I don't think this list is complete.
A great piece of news in this area, is that the upcoming SQL Server 2025 comes with a new edition: Standard Developer Edition, which removes this pain point. Not that this is going to help you today, but I still like to mention it.