Under Oribos I have an unsatisfying 98.24% under Quests because of 'Support the Court', the quest I'd get to do things in Ardenweald if I had chosen a different covenant. But I chose Ardenweald so that's not a quest I'll obtain unless I switch covenants which I won't do. Could it be filtered out by default, or an option added to support filtering it out?

Covenant filtering is being added for different things as time goes on, right now main storyline and some quests are being filtered + I think some achievs/mounts(?). Sometime later a filter setting will be added (right now it filters out by default). So this is on a TODO list, just lots of other things with higher priority.

This is actually working as intended currently... that is not a Covenant-specific quest, but rather a Shadowlands "Threads" Character quest which rewards various Personal Loot Zone Rewards for that Zone... it it likely that your current character has no way to obtain the listed rewards from that quest or Zone rewards due to Personal Loot restrictions on World Quests/etc. but that character can technically wield the missing weapons, and thus they show in the list.

To collect those appearances under the quest, you would need to take a different character through that Zone (while on the 'Threads of Fate' mode of Shadowlands levelling prior to level 60) which can receive the necessary rewards from the quest. If you can post what specific weapons are missing, we should be able to point you in the right direction for which class to use :)