I don't know of any way to get to internal logs on the Tesla Gateway, unfortunately.
Are you using InfluxDB cloud or running everything on a VM? As far as I could find in my research, InfluxDB grabs all the memory of the server it's using, so it's best to dedicate an instance to it. Note that I'm running InfluxDB 1.8. I don't know if the 2.x versions are any friendlier. I'm running both InfluxDB and Telegraf on the same VM and that seems to be working ok, but with Grafana running there too I was seeing processes getting killed occasionally by the OOM Killer. That might look the same as your symptoms.