There is a whitelist for item IDs that includes tconstruct:broadsword, but it looks like in 1.16 it was tconstruct:broad_sword, and in 1.18 it is just tconstruct:sword.

Also it may be worth considering adding an item tag for swords, so that mods and users can configure this with datapacks, though the tag system in Forge for 1.18.2 is currently a work in progress.

Thanks for the report, will look into it first thing tomorrow morning.

Released a new update.
Version Sword Displays 1.18.1-1.1.0 should now correctly support both 1.18.1 and 1.18.2, replaced the special items "whitelist" with the new tag list functionality that can be found inside sworddisplay:swords or well data/sworddisplay/tags/items/swords.json

Thanks for your suggestion ^^.