[RPG] Is Extra Attack based on class level or character level

The Extra Attack feature from different sources does not stack.

The rules for stacking Extra Attack as they relate to non-fighters and fighters are in the Multiclassing section of the Player's Handbook, pg. 164:

If you gain the Extra Attack class feature from more than one class, the features don't add together. You can't make more than two attacks with this feature unless it says you do (as the fighter's version of Extra Attack does). Similarly, the warlock's eldritch invocation Thirsting Blade doesn't give you additional attacks if you also have Extra Attack.

The only class that can expand the ability of Extra Attack to make more than 2 attacks per Attack action is the Fighter. The Fighter's Extra Attack feature says (PHB, pg. 72):

Beginning at 5th level, you can attack twice, instead of once, whenever you take the Attack action on your turn.

The number of attacks increases to three when you reach 11th level in this class and to four when you reach 20th level in this class.

Given that the option to Multiclass is explicitly an optional rule, any text within a class referring to level is always referring to levels in that class.

The chapter on Multiclassing explains what changes when you allow characters to have multiple classes, but with the exception of Spellcasting (which is explicitly called out in that chapter) everything else is dependant on the levels in the class granting the ability.

Note also, that the features for each class are shown in the Class Features table, which are specifically for members of that class. All the basic explanations for features are written as "at Xth level" because they are in the specific class section for the class they are for. Only abilities that grow or change with your level call out "in this class", because it's possible to gain a level in a different class, but you would always be referring to that other class' features table to see what happens to your character.