Adj. + 到 to express an extent
Your understanding is mostly right
“A 到 B 了” means &quot;become so A that have got into the condition of B&quot;

A: adj, but used as a verb, which means &quot;become A&quot;
B: a condition

&quot;只能吃土&quot; is a 状态 (condition) so it is the same as &quot;只能吃土的状态&quot;。
&quot;到~&quot; means &quot;getting into&quot; a 状态.
&quot;了&quot; means finished. There might be no &quot;了&quot;, depending on the tense.
Correct example:

我很穷，（已经）穷到只能吃土了
我很穷，（已经）穷到只能吃土的状态了
赌博会让你 穷到只能吃土
赌博会让你 穷到只能吃土的状态



Is it in fact a structure to create such sentences?

Yes

只能吃土的状态了 - I don't even know if I should treat it as a sentence or as a noun. So: what should come after 到?

As discussed above. 只能吃土的状态 is a 状态 which is a noun. 了 is following 到 indicating the tense.

Is this sentence correct? 累到不会走路的状态

Correct, but not a complete sentence. Missing subject and tense indicator.

Is this sentence correct? 累到不会走路

Correct. Same as above

What's the difference between 穷到只能吃土的状态了 and 穷得只能吃土?

In 穷到只能吃土的状态, 穷 is an adj. but used as a verb, followed by the extent of this verb.
In 穷得只能吃土, 穷 is just an adj. followed by an adverb.
Both are correct and mean the same.