Dear Shawn,
I think that the best way is to use PowerApps to customize the list item form so that users can check whether the attachments exist in the Custom Approval library before they trigger the flow manually.
If you have PowerApps in your environment, you can see the following example.
Go to the DocumentSubmission list, click on Integrate>PowerApps>Customize forms to access PowerApps.

Add a text input control by clicking on Insert>Text input. In my environment, it is TextInput1.

Type the notification text such as "Please check attachments' names in the next screen!" on Default to notify users to go to the next screen to type the attachments' names and check whether they have existed in Custom Approval by a search box.

Create a button such as Go to next screen for users to go to the next screen to check the attachments' names. Click on Insert>Button. In my environment, it is Button1. Type the formula Navigate(Screen1,ScreenTransition.Fade) on OnSelect on Button1.

Next click on New screen and add a blank screen. In my environment, it is Screen1. Click on Data>click on + Add data>search SharePoint and click on SharePoint to connect Custom Approval to PowerApps.


Then click on Tree view>click on Insert>Vertical Gallery to insert a gallery. In my environment, it is Gallery1.Select the gallery and select the layout as Title and subtitle and choose ThisItem.'File name with extension' in Subtitle2. Click on the first row of the gallery>insert Insert>Text input and type text "File Name and extension" on it and format it as you like. In my environment, it is TextInput2.



Click on Screen1 and add a text input control and add a search icon to create a search box for users to type the attachments' names and check whether it exists in Custom Approval. In my environment, it is TextInput3 and Icon1.


Select the gallery and type the formula Search('Custom Approval',TextInput3.Text,"{FilenameWithExtension}") on Items on Gallery1.
Add a button such as Back to Submission Screen in Screen1 for users to go to back to the form submission screen to change the attachments if it is needed. In my environment it is Button2. Type the formula on OnSelect on Button2.
Finally save the app and click on Publish to publish it to the DocumentSubmission list.

Result:


Welcome to share any updates when you have time if you need further help on this issue.
Thanks for your effort and time!
Sincerely,
Cliff | Microsoft Community Moderator