you are not learning the spells on lvl up but rather writing them down into your book. since you have 6th lvl slots you can prepare 6th lvl spells meaning you can learn 6th lvl spells. Pg. 114 has the rules for copying wizard spells into your spell book all it cares about is if you can prepare the spells of that lvl and on the same page when it lists preparing spells it states that you can prepare any spell that you have slots to cast.
PHB Pg 114, 2nd paragraph
“Copying a Spell into the Book. When you find a wizard spell of 1st level or higher, you can add it to your spellbook if it is of a spell level you can prepare and if you can spare the time to decipher and copy it.”
PHB pg 164, spellcasting, 2nd paragraph
“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. If you are a ranger 4/wizard 3, for example, you know three 1 st-level ranger spells based on your levels in the ranger class. As a 3rd-level wizard, you know three wizard cantrips, and your spellbook contains ten wizard spells, two of which (the two you gained when you reached 3rd level as a wizard) can
be 2nd-level spells. If your Intelligence is 16, you can prepare six wizard spells from your spellbook.
