I simply can't fathom the difference between
während dem Essen
Found totally nothing on google or reverso
Your example structures are functionally equivalent.
You asked about the difference between beim and während.
Während can be preposition or conjunction, just like the English while, meaning during the time or whereas respectively. You are talking about the preposition.
The preposition während is governed by the genitive case (während des Essens), but note that it can also be governed by the dative case (während dem Essen), mostly in colloquial language. Your example is correct.
A few more examples:
Während dem Konzert wurde bei ihm eingebrochen. (time of the concert)
Während der Ferien sind viele Hotels teurer als sonst. (time of holidays)
In neither of these examples could während be replaced with bei / beim / bei den, because they explicitly refer to a period of time, and the preposition bei cannot do that!
Beim is the contraction of the preposition bei and the article dem (dative singular of der or das).
The preposition bei (and therefore: beim) doesn’t refer to a pepriod of time. Instead, it tells us about a location or an event (there are other prepositions that do this: auf, in etc.).
Wir treffen uns beim Konzert. (event)
Beim Rathaus ist heute eine Demo. (location)
Beim is also often used with nominalized verbs, like in your example: beim Essen. All verbs turned into nouns become neuter: das Essen, das Laufen, das Naseputzen, das Schreiben…
This is the reason why there are so many constructions like the one in your example. All verbs turned into nouns take the same beim:
beim Essen, beim Schlafen, beim Naseputzen
By creating the noun Essen from the verb essen, you make it into an event.
Beim Essen wurde auch getrunken. (event)
Beim Tanzen hat er seine Frau kennengelernt. (event)
So, when you say
you are actually saying: At the event of eating. When you say
Während dem Essen… / Während des Essens…
you actually say: While eating.
In the case of your examples, these are functionally equivalent.
Both words are very similar and can often be used interchangeably. Imho, there is a slight difference though:
refers more to eating in general, e.g.
Pack beim Essen dein Handy weg.
Put away your phone while you eat.
or analogous to "at work"
refers more to a concrete event
Während des Mittagessens fiel mir das Handy aus der Tasche.
My phone fell out of my pocket during lunch.
analogous to "during work"
"Essen", in the first case, defines the act of eating, unless the intended meaning is "adjacent to the food/meal". Best understood as "while eating".
"während dem Essen" clearly refers to "Essen" meaning a mealtime or banquet/formal meal, so it is best understood as "during mealtime", "during the banquet". If "while eating" was to be expressed with "während", the correct phrase would be "während des Essens"