It's variously taken 1 hour, 6 hours or a day to update the lodestone. Perhaps the search indexing takes even longer. It's very normal that SE is slow in general. If it's SE, it's slow.

That's true for everything. The lodestone, mog station mails, sending out email codes, the bottleneck server queues that let 1 player in at a time (when 2,000 people are trying to get in), adding quality of life that a lot of people could code in under an hour regardless of the code structure, the battle system that snapshots damage ages in advance even compared to the mobile version, etc.