Alright, it seems like I've found the solution, or at least one of them, by following Shaun Curtis's recommendations. The thing is, even though I needed the Wrapper, I was also missing some directives in my RCL project. So, I created a file in the root of my RCL project called _Imports.razor and added the following:
Configuracion -> _Imports
@using Microsoft.AspNetCore.Components.Web
@using Microsoft.AspNetCore.Components.Web.Virtualization
This way, my buttons went from looking like this:
To looking like this:
Which achieves what I was aiming for—a way for events to be recognized. After this, I simply used a Wrapper in my Blazor project that contains the route where I want to render this component and, lastly, the component with the rendering mode I want to use:
Wrapper looks like this
@page "/configuration/ui/general/general-configuration"
<ConfigurationComponent @rendermode="InteractiveServer" />
And with that, it allowed proper interaction: