Hi Jord,
For error capturing, you'll need to catch them server-side. It depends on what you are trying to see, for instance, I've got the Mendix logs shipping from multiple instances into Azure Log Analytics.
Basically, you can use the Azure Monitor SDK within a javaagent, this provides far better customization of the received logs IMO. You can use OpenTelemetery javaagents from the monitoring companies such as Azure Monitor, Dynatrace, NewRelic, they all have them, failing that you can create them in java.
There are many ways to get logs into Azure Monitor, as mentioned above, or through APIS and DCR, DCE, etc.
I use Microsoft's OpenTelemetry Java Distro application to get all the logs from the Mendix logs in real time, near real time, runs about a minute behind, but that's to do with Azure's ingestion. I'm doing this on versions 10.21.0 and above. No idea about Mendix Studio 9.x