Geromino: Wizards (and other spellcasters) are not supposed to be able to change spells as quickly as they can in BG, but otherwise its as the PHB specifies:
"When you find a wizard spell of a level for whicvh you have spell slots and you can spare the time [... you can copy it into your spellbook]"
PHB pg 114
That's from the Wizard class description? For a single class Wizard, the spell levels they can know and prepare correspond to their spell slot progression. So whether you consider 'know and prepare' or spell slots separately or together, a Wizard 1 will only be able to know and prepare 1st level spells.
I don't have the PHB so I can't quote from it but I think the SRD should be the same with respect to multiclassing. According to
https://5thsrd.org/rules/multiclassing/#class-features, which corresponds to the official document at
https://dnd.wizards.com/resources/systems-reference-document, 'know and prepare' and 'spell slot progression' are treated independently:
"Spells Known and Prepared. You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class"
Therefore, a Cleric 8/Wizard 1 will only be able to know and prepare the spells that a Wizard 1 can, namely 1st level spells.
"Spell Slots. You determine your available spell slots by adding together all your levels in the bard, cleric, druid, sorcerer, and wizard classes, and half your levels (rounded down) in the paladin and ranger classes. Use this total to determine your spell slots by consulting the Multiclass Spellcaster table.
...
If you have more than one spellcasting class, this table might give you spell slots of a level that is higher than the spells you know or can prepare. You can use those slots, but only to cast your lower-level spells. If a lower-level spell that you cast, like burning hands, has an enhanced effect when cast using a higher-level slot, you can use the enhanced effect, even though you don't have any spells of that higher level."
As already covered, spell slots progress based on character level but this section states nothing about being able to know or prepare spells of a particular level. That aspect is already covered by the 'Spells Known and Prepared' clause.
Nothing in the multiclassing section explicitly mentions anything about a Wizard's ability to copy spells, although I'd be inclined to consider a copied spell to be a known spell. However, even if you treat them differently, a Wizard 1 wouldn't be able to cast 2nd level and higher spells, even if they could copy them.
Thematically, the restriction makes sense to me. A Wizard 1 single class is a novice Wizard and Wizards acquire their spell casting via studying. Gaining many levels in a divine spellcasting class such as Cleric shouldn't magically, pun intended, grant the character knowledge and ability to cast higher level Wizard spells.
Mechanically, though, I find the restriction overly onerous, which is why I like how it is in BG3. Loosening the restriction makes a multiclass Wizard much more flexible whilst IMHO not making them overly powerful since the Wizard class level still restricts the maximum number of spells they can prepare and their class feature progression such as arcane recovery and the total character level restricts the available spell slots. In BG3 specifically, it allows me to create a Bard that can prepare some spell slots with the flexible spell selection of a Wizard, whilst not having all of the full power of either a single class Bard or Wizard.