You want a router with SNMP logging. Since I know of no list that explicitly calls this out, look for routers that run or optionally give you the choice to install DD-WRT.
DD-WRT setup is widely documented so I won't duplicate efforts on that.
https://www.howtogeek.com/141135/it-geek-monitor-network-devices-with-snmp-simple-network-management-protocol/
In parting, share your current model so I can check it out.
Hello! Does anyone know of a newer router that allows the direct exportation of logs into a client such as Link Logger? I used to be able to do that with a Linksys router, but unfortunately the new web interface does not allow this particular type configuration. I have tried researching this but am having trouble finding this specific information.

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