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A過去の通知はありません There are no past notifications

B参加予定のイベントはありません There are no planned events.

C(あなたは)メッセージがありません You have no messages.

In A and B, it can either be the main topic or the contrastive は as in:
(あなた(に)は)過去の通知はありません。 This would emphasize the ない. I think it is definitely
the former (hence my translations), as it is a general statement that there
are no past notifications. I think that “you have no past notifications” kind
of sentence would have to be written as C so it would be clear that (あなたには) is
implicit.

Also in:

A 私(に)は財布はない “I do not have a wallet” 財布は is contrastive, 私(に)は is the main
topic

B 私(に)は財布がない the same as A, but the emphasis is not on ない

Or is it more like 財布は私に(は)ない with the 財布は as the main topic? 財布が私に(は)ない would
then be the 現象文? は optional as a contrast.

Without 私は and any context, 財布はない seems like a general statement that there
(somewhere) is no wallet. Or reversed; そこには財布が(は)ない with そこには as the topic.
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particle-は
Which は is this?
You have to think a bit differently when a negative sentence is concerned. In
a negative sentence, は is the default choice (See: [Why is the topic marker
often used in negative statements (ではない,
～とは思わない)?](https://japanese.stackexchange.com/q/1077/5010)). Aはない/Aはありません is
"There is no A" stated as a **known** fact (I don't know if this は is
contrastive or thematic). On the other hand, when someone says Aがない/Aがありません,
this is a [現象文](https://japanese.stackexchange.com/q/43213/5010). It tells "A
was not found" or "A is missing" stated as a **newly found** fact.

You seem to already know those basics, so let me explain the difference using
examples.

In a typical message list UI, メッセージはありません and メッセージがありません are almost the same,
but the latter sounds like the system searched for messages and just noticed
there was nothing.

On the other hand, メッセージがありません is the only choice as an error message shown
after a user clicked a "Send" button, because it's a newly found fact noticed
only after the click. Likewise, most unpredictable error messages use が (e.g.,
通信が切断されました, ストレージ容量が不足しています, ファンに異常が発生しています), while some error messages use は
(このディスクの再生はサポートしていません).

財布はない and 財布がない sound very different to native speakers. Besides, when there
is another は-marked argument working as the topic, the story is totally
different.

  * 財布はない。  
I don't have/use a wallet. / There is no wallet.  
(Stated as a known fact)

  * 財布がない。  
My wallet is missing!  
(Typical 現象文/中立描写文)

  * 私には財布はない。  
I don't have a wallet at least _(but I use something else)_.  
(The first (に)は is thematic, the second は is contrastive)

  * 私には財布がない。  
I don't have a wallet. / There is no wallet I use.  
(The first (に)は is thematic, the が is a simple subject marker. This is a
typical "double-subject" sentence.)
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