Now then, see, if you will, you need to understand the wizard.
Wizards are extremely full casters and rarely gain anything from multiclassing. If you decide to multiclass, I highly suggest that you do it around lvl 18-20 as you will be able to measure what's more important.
Cleric gives you access to healing spells and if you choose life domain, you get ...
As Dale M notes in the question you linked, pg 164 of the Player's Handbook has the answer:
You determine what spells you know and prepare for each class individually, as if you were a single classed member of that class.
So a level 10 Wizard/level 10 Arcane Trickster has 9 cantrips in total, 5 from Wizard, 4 from Arcane Trickster.
There are a couple of parts here. The short answer is that you're still limited to illusion/enchantment spells when taking Rogue levels, but can copy any spell you can find (within level constraints) to your wizard spellbook.
Arcane Trickster spells
When you take a level in Rogue and get new spells, you can only choose spells from the Enchantment or Illusion ...