So most of us know that after Mycenaean Greece collapsed, their dark ages started. But what confuses me (as someone just learning about this age) is if they really forgot how to write or not.
Some refer to the Middle Ages as the dark ages, but that’s because of the lack of writing that we have from the period, and the decline of information. That doesn’t necessarily mean that they didn’t write, they did, it’s just we don’t have too many records.
Is it the same for Mycenaean Greece after their collapse, or did they actually forget how to write? That simplifies it a LOT, as I know that they didn’t just forget their writing, but after time did they forget or no?
Yes, they did, and yes it is pretty straightforward. 'Forget' is perhaps a misleading way of thinking of it, though. In the Bronze Age, the only function of the Linear B script was in the functioning of the Mycenaean palace culture -- in its economic administration. When the palace culture collapsed, that function ceased to exist. So I'm not sure 'forgetting' is the best way of describing what happened.
Think of it like, say, shorthand. Shorthand was a skill that was needed in the western world in the 18th-20th centuries for certain stenographic functions. It was largely confined to those specific functions. Once technology arrived that made it unnecessary, the skill waned, and by now it is a rare skill, abandoned except by a few enthusiasts. I'd guess even those enthusiasts would agree that it's likely to die out altogether at some point in the not-too-distant future.
The Linear B script was a similar kind of technology. It was used for specific functions. Once those functions disappeared, so did the writing system. The alphabet that developed 400 years later, adapted from the Phoenician script, ended up being much more successful because it was much more versatile. It started out being used for dedications, epitaphs, and graffiti in the 8th century; later it came to have more official functions too, used for governmental inscriptions, and larger-scale functions like books. And that's why it has persisted to the present day -- because its versatility, and the ease of learning it and using it, meant that it wasn't confined to a limited range of functions.
For some further reading, I'm not certain what the best thing to recommend would be: the entries for 'Alphabet' and 'Pre-alphabetic scripts' in the Oxford classical dictionary are pretty limited and don't talk about social function. For the rise of the classical-modern alphabet and its functions, the introductory chapter in the book Written texts and the rise of literate culture in ancient Greece (edited by Harvey Yunis, 2003) is pretty good. For the use of the Linear B script, something like the first volume of A companion to Linear B. Mycenaean Greek texts and their world (ed. Duhoux and Morpurgo Davies, 3 vols, 2008-2014) might be the way to go, though it's a bit full-on.