What you see in the loading dialog has nothing to do with the Navigraph database which is perfectly fine for 2308. Just checked.
This dialog shows the number of ILS loaded from the MSFS simulator scenery library. I see only 4441 ILS for MSFS but still have to check with the latest beta update. Maybe an add-on interfering?
Some more details about the issue:
There was an error in LNM which reads the ILS from the .../Community/navigraph-navdata-base... which it should not do. The preferred way is to ignore navaids from the Navigraph MSFS update and use the LNM navdata update instead.
In any case this does not affect LNM (no duplicate or wrong ILS shown) if the right scenery library mode is used (51. Load Scenery Library — Little Navmap User Manual). The mode is selected automatically with the latest release.
So if LNM reads the Navigraph data directly, do I still need to perform a LNM Load to update the database for each new AIRAC, or does the Navigraph updater put the data in the correct place already?
LNM does not read the Navigraph data to be precise. You install a read-to-go database for LNM using the FMS Data Manager.
Reload is recommended if you updated add-on airports or in case of MSFS updates.