On my website I want to build a .NET Core application which invokes the SharePoint Online search engine (using REST Service) while also meeting specific filtering conditions regarding the managed properties.
I've searched for this but only found information on CSOM.
Are there any .NET Core examples on how to utilize SharePoint search and the advanced/dynamic filtering part on this?
In the past search had its own endpoint, currently MS is moving things to graph. There is an open source project on GitHub that may give you the features you look for https://microsoft-search.github.io/pnp-modern-search/
In general if you want to work with SPO/Graph you need to use the SDK. here you have some references https://docs.microsoft.com/en-us/sharepoint/dev/sp-add-ins/using-csom-for-dotnet-standard
HttpClientshould be pretty straightforward, assuming you can authenticate and issue simple REST calls. The documentation should be able to provide you with what you need to enable filtering. Give it a shot and come back here with a more specific question when you get stuck.