Wow this is all super helpful, thank you for taking the time to go into it for me. I really appreciate it. If we were looking past immediate benefit would you still suggest the Solar Pearl? Abstract question I appreciate, but just want to be sure that I'm pulling the one that's best longer term. Mainly because I notice Ningguang wasn't a steadfast recommendation in the team comp, but then again if I've already got solid weapons for the others I suppose it's worth having that great catalyst in general.
I don't think there is a "must" priority order on the pass weapons at all, only what you need
Ningguang isn't of any use to your teams so I would strongly recommend against the Pearl especially as you have Widsith, catalyst users also have the 3 star fantastic weapon "Thrilling Tales of Dragon Slayers" so catalyst users are not struggling for good weapons
To me claymores and spears probably have the most restrictive regular weapon pools
You only have Xiangling for spear though and you have good options so Deathmatch isn't worth it (also next patch has a free ER spear)
Serpent Spine is great for any DPS claymore user like Beidou freeing up the energy recharge weapons for Chongyun and Sayu, (there is a free claymore next patch that has an elemental burst DMG bonus though)
Black Sword is a great weapon, but you have Mistsplitter, so you probably don't need it right now (but it is great on many characters in the long run)
Viridescent Hunt is a good pick for Fischl/support archers, but again you have Thundering Pulse so you probably have decent bows freed up
