The film "Valkyrie" (2008) depicts that while Stauffenberg was on his way to Berlin, Friedrich Fromm called Keitel to ask him about the rumors circulating in Berlin about Hitler's death.
Fromm to Bendlerblock operator: Yes, get me the Wolf's lair.
Fromm to Wolf's lair operator: Yes, general Fromm ; field marshal Keitel ; urgent.
Fromm to Keitel: Yes, I am, I am sorry to, a, disturb you sir but I wonder if you could tell me what's happening; most incredible rumors are circulating in Berlin.
Keitel: I don't know what you mean.
Fromm to Keitel: There is talk that the Fuhrer has been assassinated.
Keitel: Another failed attempt - the further was never in danger; by the way - where is your men Stauffenberg?
Fromm to Keitel: Stauffenberg, he, he('s?) on his way back to Berlin I would think.
Ketiel: Let me know when he arrives, I'd like a word with him (hangs up).
The following depicted phone call is very "cold" ; no hello, no goodbye; just "yes" for start and hanging up without further notice of finishing conversation.
I don't know about phone call manners in the 40's anywhere, but:
Did the Nazi Army have a telephone conversation pattern?
That is to ask; did officers avoid starting with "hello" and finishing with "thank you" and "goodbye" in the end of phone calls in general and if so was it because of a "commander-commanded distance" and maybe also other reasons?
They had the general directive H.Dv. 95/13 Der Feldfernsprecher 33 (Heeres-Druckvorschriften) (no digitised version available, current physical copies in corona lockdown).
But that is probably not really what you look for. Apart from deducing anything from a Hollywood movie about nazis… That is in general just not a venue of inquiry to learn much of anything.
It seems more fruitful to look into 'Prussian officer's jargon' and speech style. Admittedly being more of an issue of sociolinguistics.
While the movie just focusses on making a general 'military' impression, the actual speech style of that army was still very much the Kaiser's army one. Full of ellipses and fragments. Shortness, brashness, flippancy, nominal style. Sometimes a tiny bit subverted if Saxon, Bavarian or Austrian officers were involved?
In the actual situation of a conspiracy fueled assassination attempt and coup d'etat, it seems also quite impractical to focus anything into the redundancy of politeness. After all, any telephone user, including private ones, was issued this directive:
(img-src, "Nimm Rücksicht auf Wartende. Fasse dich kurz!"
(Keep it short! (ie efficient))