Learn English – Being someone’s pet

Eager beaver and more catholic than the Pope are nowhere near synonyms.

The Free Dictionary definition may be misleading when it says an eager beaver is often excessively industrious. The term is often used approvingly, or with no particular value judgement implied. But more importantly, eager beaver can be applied to anyone who's keen to get on with anything. I imagine it owes most of its currency to the alliteration.

On the other hand, more Catholic than the Pope is always pejorative and/or exaggerated, and never applies to anything other than a person's (specifically, Catholic) religious faith (although there is the closely-related rhetorical question "Is the Pope a Catholic?", light-heartedly meaning "Definitely yes!").

She wrote a true crime book a few years ago that I quite enjoyed. That’s pretty much all I read.

• "That" = true crime
• "pretty much" = almost completely (as you said)
• "all" = the entirety
• "I read" is the present

So it means:

True crime is almost completely the entirety of what I read

or, to rephrase:

When I read books, they are almost always "true crime" books

Note that the "that" in your quote almost certainly refers to "true crime" in general and not to that specific book. This is because the "I read" is present, rather than the present continuous "I'm reading". It is unlikely that someone constantly repeatedly reads a single book, unless they are extremely dedicated to it for some reason (such as a devout Christian who only reads the Bible, or an obsessive quiz lover who only reads the encyclopedia).