What is the function of 好 in 你好厉害 and 我好无聊?
So, I dug out my Modern Chinese Practical Grammar Analysis 現代漢語適用語法分析（下冊) and it turns out that those expressions do not exist.
Under the section on &quot;adverbs expressing degree&quot;, it lists 比較，相當，很，十分，非常，極爲，極其，最，...極了 ，太...了， 可... 了, 挺...的，真...啊，怪...的, 夠...的，特別，尤其，更，還，... but not 好...or 蠻 (simp: 蛮）
Except of course, that 好 very much exists, and is just another (colloquial) way of expressing degree in Chinese, just like 挺, which could be considered its northern dialect equivalent. The same answers apply here as in this question. Wherever you can use 很 you can technically use 好. This also means that sometimes it doesn't need to be translated in English:

你好厲害啊!/你好厉害啊！  You are (so) amazing!
這道題好難哦！/这道题好难哦！This question was pretty hard!
得到批准好不容易啊 I (really) struggled to get approval. (this one has
special constructions with 才, as you can see here

Note that the full expression is often &quot;好 (something of which there is &quot;a lot of&quot;) 啊/哦/呀&quot; as in the examples above, which further indicates a more colloquial/intimate nature. In the two sentences below, I'd always pick 很 for the first one and 好 for the second one.

我很喜歡在中國旅游/我很喜欢在中国旅游。I very much enjoy travelling in China
我好喜歡你啊! /我好喜欢你啊！ I really like you

To wrap up, 好 seems to be just how southern Chinese languages/dialects, e.g. Cantonese, say 很. Chinese &quot;dialects&quot; are always felt as more intimate and less formal than the standard language. Teaching materials may avoid (southern) dialectal terms at all costs even while including stuff like &quot;極了/极了“ which you won't see outside of some subtitle translation.
But most southerners speaking Mandarin casually (not even 塑料普通话）will say something like 好好吃啊！ (or 蠻好吃的!) rather than 很好吃！ Even northern Chinese have adopted 好 precisely for that informal or perhaps southern/soft/可愛 feel and will exclaim things like 我好餓啊!, even if they tend to use 很/挺 a lot more.
So feel free to use 好、很 、挺 as you see fit!