Finally found what the problem is. Might be useful information for others and something for the dev-team to tackle.
I had two different types of deployments to the Azure Web App: one from VS2019 using Web Deploy and the other was in a YAML script in an Azure DevOps pipeline. Turned out that the web deploy is doing a FILESYSTEM deployment, but the pipeline is doing a PACKAGE deployment. In the last case a zip-file is copied over (has a lot of benefits) and the Azure Web App is set to run from the package.
I think in the situation of using a PACKAGE, that the logic in the Syncfusion libraries to load an external DLL is using a call that doesn't take this package-use into account. Therefor the load of the extra DLL's fail. Switching to FILESYSTEM deployment and everything works.
Would have saved me a lot of time if the error raised by the Syncfusion DLL's would have more details about the load error though!