Whether the use of the workbench in a production site will have negative effects on the performance of the site depends on what the web part you are testing does. For example, if you're just getting some a few dozen list items from a couple lists and rendering it out on the page, then you will be fine. But if the web part gets tons of data from multiple sources to build some sort of visualization, it could have some impact. Similarly, if the web part makes changes to the site configuration, that could have an impact (particularly if there's a bug in the code you're testing).
I highly recommend that you consider using a developer tenant to test your web parts instead. You can get a free developer tenant by joining the Microsoft 365 Developer Program. I've been using developer tenants for all my SharePoint, Teams, and Power Platform development for years.
I hope this helps.