I already had a Unity web (HTML+WebGL+webassembly) game with pay-what-you-want downloads but just to be sure it works I tried setting it to Paid and the page does explicitly say the web version is still freely available.
https://technicat.itch.io/learnunity
But I've seen anecdotal reports and in my own experience web games generate less contributions than downloadable games-- I don't know ifthat applies to this scenario, but if it does, an alternative is to have one page just for the web demo and one for the paid download and have them link to each other.
I've seen Unity apps have this feature (in particular LittleShopOfJunk). They have a fully playable game on the browser and a Unity app that you can download as well. However, I don't use Unity for my projects so not a possibility for me as I think it's a property of the Unity "Kind of project".
But having two versions, one for the demo and one for the full project, is something I haven't considered, might work as a backup plan!
Just FYI, in case you're not familiar, Unity is a cross-platform engine (like Godot, Unreal...even Ren'py) so in theory most of what you build and script is platform-independent and you can take a single project and tell it to make different builds for the supported platforms which in the case of Unity is web (HTML+WebGL+Javascript+WASM), Windows, macOS, Linux, Android, iOS... and thus you can make the most of your development effort. In practice however, there are platform differences like performance constraints for web, screen size, performance issues and touch input for mobile, etc. and you typically end up writing different code for different platforms distinguished by compiler defines
https://docs.unity3d.com/Manual/PlatformDependentCompilation.html
Also it's a lot of work and expense to test every single platform, so a developer might just focus on one or two.
