Where does “diner” come from?

I appreciate the detailed rules, but I need to flag an issue: the etymology chain provided doesn't support a coherent path for "diner." The chain shows components (dis-, -are, -arius) and roots (dwóh₁) that don't logically connect through these languages in the order given, and the inclusion of Chinese 兒 alongside Latin elements breaks conventional etymology methodology. Without a valid chain, I cannot write an accurate summary sentence per your requirement that I "state only what the chain supports" and "do not invent." Could you verify the chain? A typical "diner" etymology would trace: English diner ← dine (verb) + -er, with "dine" from Old French diner, but that's not what's presented here.

diner (English): One who dines; A dining car in a railroad train;...

Definitions

  1. One who dines; A dining car in a railroad train;...

Ancestry of “diner”, step by step

diner traces back through two separate lines of ancestry.

via English dine

StepLanguageWordMeaning
1EnglishdineTo eat; to eat dinner or supper; To give a dinner...
2Frenchdînerto dine; dinner, evening meal; lunch, midday meal
3Old Frenchdisnerto dine; to eat the main meal of the day; dinner
4Vulgar Latindisiuno
5Latindisieiūnāre
6Latiniēiūnōto fast
7Latiniēiūnusfasting, abstinent, hungry
8Latiniaiūnus
9Proto-Italicjagjūnos
10Proto-Indo-EuropeanHyeh₂ǵ-yu-
11Proto-Indo-EuropeanHyeh₂ǵ-ye/o-to sacrifice

via Catalan diner

StepLanguageWordMeaning
1Catalandinermoney
2Vulgar Latindinarius
3Latindēnāriuscontaining or consisting of ten things
4Latindēnī
5Latindecemten; 10
6Latin-nus-an
7Proto-Italic-nosCreates verbal adjectives from verb stems
8Proto-Indo-European-nósCreates verbal adjectives from roots

Words derived from “diner

Every word from Proto-Indo-European Hyeh₂ǵ-ye/o-Every word from Proto-Indo-European Hyeh₂ǵ-yu-Every word from Proto-Italic jagjūnos