Most viable way to farm Mana Prisms

Repeat the 30AP exp card Daily Quest to earn 3-star exp cards to burn.

You should be able to get half of what you need from the event shops and lotteries though.

Aside from participating in events, which frequently provide a few hundred mana prisms, the most efficient method I know of is doing the 30 AP quest for Silver experience cards. Those can be burned in the shop for 1 Mana Prism each, and you'll usually get 7-9 per run. If you have your 3-star servants ascended already, you can also burn extra copies you get from the Friend Point and/or Quartz Gacha for more prisms.

Mana Prisms are most efficiently collected over time. It's hard to rush them without mind-numbing amounts of grinding, so it's better to collect as you go if you can. (This is, of course, a bit inconvenient for those who start the game with something they want nearing its deadline...)

You can always easily get all 5k prisms needed for Shop CEs from events if you won't spend them on fous and EXP cards, of course
But if you want it asap then yes, 30AP ember quest is your best option