Dump the logs into elastic, loki or whatever, along with pod name as a label. Usually I use Kibana, so I don't want to speak for Loki, but seems pretty straight forward.
Kibana is ok (definitely beats grep) when you want to look across a fleet and determine if a specific thing is happening. But when you have a specific symptom that happens on a particular instance, what you want to do is see logs in the order they happened, and Kibana isn't close. Querying and viewing logs are just slow and cumbersome relative to less/grep.
Best to configure view for this to limit columns and maybe pre-configure some filters. Plus annotate your logs with timestamp, so you rely on time of event and not time of ingestion.
But these both are one-time configuration thing and then you can simply scroll.
What's missing is that I don't want to learn and use some clunky web UI in order to do this. I want the UI to be "download this text file" and then use the tools I already know and understand (local text processing utilities and text editors)