Jisho

As I see it, and I am no expert, suru verbs are not actually "verbs" but nouns. The only difference between a "pure" noun and a "suru verb" is that the Japanese people do not attach する to some nouns belonging to the first group but they attach する to those nouns of the second group, just because yes, that's the way it is. I mean, as long as some japanese verbalise a noun by attaching する it may be considered a する verb regardless of what a dictionary may say. My point is that when jisho.org says that a noun is either a する verb or not it should be seen as a guide of how the word tends to be used rather than a categorical classification. Another example, the word アンケート (questionnaire, survey) is listed as a noun only but I think アンケートする makes perfect sense anyway. I'm rather sure we could find more examples on that.

Now, regarding the word 手伝い, I would see it as a nominalisation of the verb 手伝う by taking its 〜ます stem. 手伝う → 手伝います → 手伝い. However, I don't know if there are particular rules to nominalise verbs this way or not. Looks like someone else had this idea as well and asked here: https://japanese.stackexchange.com/questions/59902/verb-stem-vs-の-nominalizations?rq=1

Also, bear in mind that what looks like a suru verb in the construction お手伝いする (note the お) is the standsrd way to conjugate a verb in the humble form, which can be confusing too (for more in this look at the 5th point of this article: https://kawakawalearningstudio.com/all/what-you-need-to-know-about-japanese-verb-stem/). However I've searched the #sentences for てつだいをする myself and there are some of them where this is not the case anyway (click here for the results of this search, you will get some example sentences that may help you grasp the meaning of 手伝いをす: https://jisho.org/search/手伝いをする%20%23sentences ).

BTW, this question reminds me I have never understood why the particle を is replaced by の when making subordinate clauses with suru verbs, it has always freaked me out but it's just how the Japanese do it.

I mean, to convey "he helps his mother" I would say:

彼はお母さんを手伝いする。

But in fact, Japanese say:

彼はお母さんの手伝いする。

Lol.

Sorry, I re-read your question and realised I didn't give you a an answer in my previous comments. As you, I haven't been able to find example sentences where 手伝い is used as a noun, either. As far as I understand it, it is always used in the structure Aの手伝いする conveying "To bring the help that A needs". So, my guess is that Maryの手伝いする is "［someone］helps out Mary".

Both of the example sentences listed in the Jisho entry use it as a noun, so I'm not sure where the confusion is coming from.

@Leebo, if you look at the example sentence in the first meaning of the entry, it is undoubtedly used as a noun (conveying "the person who helps"). However, I'm not sure where you see 手伝い as a name in the example sentence of the second entry. I see a する verb.

「台所でお母さんの手伝いをしていたの。」

Maybe you could help us to understand what you mean? Probably the confusion comes from the second meaning of the entry and its example sentence.

In 手伝いをする, 手伝い is a noun. Just like any other noun with を and some other verb after it.

A suru verb can have する connected directly to it.

Take 宿題 (homework). 宿題をする means "do homework." You can't say 宿題する though. It's a noun and not a suru verb.

手伝い is like 宿題. You can't say 手伝いする.

You mentioned お手伝いする, but this is different from 手伝いする.
お手伝いする is a keigo version of 手伝う, not a suru verb form of 手伝い.
Almost any verb can undergo the same conversion, excluding ones that have special keigo forms.

Oh, and two more comments.

Rather than be a suru verb, you'd just use 手伝う as a normal verb to say help.

Because Japanese people often omit particles in casual language, you could potentially hear what sounds like 手伝いする. I can't say you won't hear it. But this would be casual speech if someone said it, not textbook correct grammar.

I understand. Thank you.