Unrelated to Latin. I speak four languages, each learned in a totally different way.

The fastest that I've learned a language was by buying a grammar and spending hours on end doing grammar exercises. It doesn't just work by "traditional academic metrics", it works and fast. That's because it's faster to learn something if you're explicitly shown the pattern and then you do repetition, than if you just do the repetition.

If you speak four languages, in most countries you are an outlier, and you should not assume that what works for you would work for others.

Of course you need to do grammar exercises, the interesting question is whether it's good to avoid your native language when exercising, as Lingua Latina per se Illustrata does but most language training materials don't.

Now I’m curious; what book of grammar was it? What did the exercises look like? What other languages and strategies did you use?

As someone who also learned multiple languages, the most typical result if grammar focused classes is that you cant use the language at all for years. And yes it is consistent outcome for majority of the students.

Like, outcome of language classes you describe are people who cant watch movies, cant listen to podcasts, cant talk with natives ... but are decent in solving grammar exercises. And to add insult to injury, the whole process so massively sux, that you are likely to conclude that learning languages is not for you.