There are a number of open integrated development environments which offer developer to make and compile software, such as the replit.com platform. Will the author of the code have full rights on the software or part of it will belong to the IDE creators because of using their server?
As we have said, and as you know, if the IDE is a piece of software you download and run locally, then generally speaking the IDE's licence has no effect on the licence under which your code can be released.
If, however, the IDE is purely web-based, and offered as SaaS (software as a service), then it will depend on the provider's ToS (terms of service). There have certainly been some pretty awful land grabs in ToS history, and if the IDE provider you choose has something in their ToS that gives all rights in created code to them, well, you just gave your code away.
SaaS has a number of dangers, and this is one of them. If you don't want that, and you don't want to be reading endless ToS documents, don't use a SaaS IDE. You can read the same argument made more cogently and at more length here.