Still haven't figured out what exactly Invisibility does in contrast to just Stealth but if you can figure out a way to make it relevant it's there from the second Channel Divinity slot at lvl 6.
With Invisibility you can ignore enemy sight radiuses. Not sure if you still need some Stealth to avoid making noise, but in principle you can effortlessly approach enemies to steal / stab / always start a Surprise round.
Greater Invisibility even lets you repeatedly stab enemies while staying undetected - but you need increasingly difficult skillchecks to avoid detection after attacking (so you need heavy Stealth focus to use it reliably, preferably Expertise + Advantage; Pass Without Trace wouldn't hurt).
Anyway, if you like/want the stealthy playstyle, there are better/easier/more spammable ways. The main one being a level 5+ duergar, who gets to freely spam Invisibility outside combat (limited to 1 use in combat). This one will always break on interacting with environment/stealing/picking stuff or attacking. Durge Cloak, which self-buffs Invisibility for 3 round on kill. Then there is Gloomstalker, who can Invisible 1/per fight when obscured - and Shadow Monk - who can unlimited Invisible when obscured.
Trickery Cleric's limited use Invisibility is very humble next to those.