Difference between using 被 and the object in the topic position?
Let's answer the question by showcasing topic-comment, by defining 被 usage and then see if there is any overlap.
Re: topic-comment
Let's open with examples for topic-comment.


作业(我)做完了。 Done homework.

(你)饭吃完了吗？  Finishing eating (dinner)?

违法的事情(你)不要做。  Do not do illegal things.

这个信件，老板吩咐我亲手转交给你。 Boss instructed me to hand you this envelop in person.



The interesting thing about these sentences is that order reversal is possible for all four and the alternate ordering is probably just as likely in real life. See below.


(我)做完作业了。

(你)吃完饭了吗？

(你)不要做违法的事情。

老板吩咐我亲手转交这个信件给你。



In the alternate ordering, the sentences may put more emphasis on the earlier agent or action or descriptive quality in the sentence. (In example 4, the 2nd ordering highlights 亲手. Other examples are more obvious.) Nevertheless, re-ordered or not, they describe identical actions and are grammatical either way. Also, more alternative ordering may be possible.
Thus, one may find it efficient to identify topic and comment in these sentences and take advantage of the pattern that topic can either precede or follow comment. One may even define special topic-comment structure by this exact quality of having at least 2 possible grammatical ordering.
So, the examples above -- via virtue of allowing order reversal -- are indeed topic-comment.
That said, I really don't see an easy way to differentiate topic-comment sentences vs non topic-comment sentences. That calls into question whether topic-comment structure is truly universal. In any case, if your sentence contains a linking verb like 是. Order reversal probably cannot be done. Semantically, there is always topic and always comment. But you don't always have topic-comment structure.

Examples:
这辆车是他的。 This car is his.
平面三角形内角和为180度。Planar triangles' inner angles' sum is 180 degrees.
(Literal translation to show the Chinese structure.)

The reality does get more complicated than what is shown here. Not least because the linking verb may be omitted.
Definition of 被 structure
In the linking verb examples, you cannot use 被. So those are out of the picture.
In the topic-comment examples --- at least in my examples where the topic are noun phrase, you can always try inserting 被。A bunch of funny sentences are going to form. I want to use those strangeness to explore what 被 does.

作业被(我)做完了。

饭被(你)吃完了吗？

违法的事情不要被(你)做。

我被老板吩咐亲手转交这个信件给你。


If you have good familiarity with Chinese, you instantly recognize example 1)-3) are not sensible. Literally 100% never said. 4) is sensible but it does not have the same order as in topic-leading ordering.
So we have a conclusion: topic-comment reversal is not replicated by 被 related structure.
被 has a structure of its own and usages of its own. It is better considered as a helping word that in usage induces the following phrasal structure:
Noun phrase (optional) + 被 + noun (optional) +  verb phrase
and in meaning induces the connotations described by Li and Thompson. (All is well in their example except the word 气 is not used in a real way.)
被 signifies that the normal target of the verb phrase is not. A reflection happens. For example,

被人肉 got doxx'd
被自杀 got suicided (ie. murdered and displayed as seeming suicide)
我被辞职了 I got resigned (ie. I was fired but I totally had agency in the resigning.)

Note that the connotations here are in line with Li and Thompson's analysis.
The more flexible definition above is the more inclusive one. But for educational purpose, let's also do a more particular (limited) definition of 被:
Noun phrase (optional) + 被 + noun (optional) +  verb phrase
The leading noun phrase is the target of the verb phrase; the optional noun is only grammatical if it was the subject of the verb phrase otherwise.
If you use all components in &quot;NP + 被 + noun + VP&quot; such as in your example
热狗|被|男孩|吃了
no further order reversal is grammatical. (If you use 被 + VP only, there is nothing to reverse. But you can move this combo around freely and be gnarly with your sentences.) In other words, starting with a 被 sentence, there may not be corresponding topic-comment sentence.
Back to the earlier examples, why are they strange? They follow the same sentence structure as prescribed above and as 热狗被吃了, why are they strange while 热狗被吃了 is not strange? Those 被 examples 1-3 are not just not preferred. Their meaning appears to native-speakers self-contradictory and are never ever spoken.
Well, we really need more examples to tell here. But I have a theory for you to think about.
Without 被, the leading agent in example 1), the subject 作业 is already assumed to be passively performed by the 2nd agent. You can insert 被 in the sense that other sentences following this pattern can make sense. But semantically, this double passiveness is self-contradictory.
The same idea for 饭。 In other words, in Chinese, the words 作业, 饭, 事情 all have implicit passiveness when acted upon. 作业做 always means 作业 is the target of 做 regardless of ordering. (Topic prominence again.) Adding 被 contradicts with the inherent passiveness.
Note: 作业做 by itself is one of those things that cannot make sense with regular present tense. 作业做了 makes sense. 作业做 does not. When that happens, if you literally say 作业做, people give up on the presumed passiveness and try interpreting 作业 as the active agent or check for alternative meaning of 作业. Ofc in this case it still doesn't work.
What is the overlap between topic-comment and 被?
So far, we have not found any.
The only similarity between the two is that topic-comment structure allows for the reversal of topic and comment in a sentence, while 被 re-designates the target of a verb phrase, which in turn means that in order to produce an equivalent sentence, you need to reverse order.
Thus any similarity is coincidental.

Now we need to end with some necessary disclaimers:
One, topic-comment may not be a standalone, universal structure in Chinese. Sometimes order reversal is possible. Sometimes it is not. Sometimes multiple orderings are possible. In your example, 热狗男孩吃了 is potentially dubious by adopting a noun + noun + verb phrase structure for a verb that takes both subject and object. And I made a point about 是 sentences. Every sentence has a topic and comment. So it's difficult to differentiate what is a topic-comment structure vs what is not. I cannot conclude one way or the other whether topic-comment should be truly standalone and what its defining feature is without examining hundreds of more examples than this question. And we don't need to do that to make progress in discussing Chinese. Let's save that for the future and for over time.
Two, I used an &quot;English way&quot; to explain 被. But Englishness is ofc not the point. That is, I used phrasal structure conventions that are conventions in English and are successful in English. Phrasal structure is not a language-specific concept or tool. What I did is nevertheless not the convention in Chinese -- unless by coincidence that I am not aware of. What does that mean? It means just that: not convention; not consensus. But it may be useful and it may through coincidence become consensus when one is found and popularized.
Also curious along the same line, in English &quot;helping word&quot; really means &quot;helping verb&quot;. Helping verbs are auxiliaries appear at the same places as verbs and potentially along side them. Is 被 a &quot;helping preposition&quot;?? That would be new.
Lastly, I believe the discussion above showcases the need for neutral examples. We use examples to support our theories. We also need examples to discover theories; and to validate theories. We need to support as well as validate. That's important. For that, we need lots of examples.
So if you have more examples that can showcase points included or not yet included in the discussion above. Please comment below.