Chip.With it turning out that Skynet was based off of the first T-800's arm

Dark Fate basically did that. Skynet no longer exists, (arguably) mostly thanks to time-meddling*.I'm a little surprised we haven't gotten a storyline like that yet in the franchise.
Nothing is done with the notion though, the movie lazily just has a Skynet substitute named Legion.
*If Skynet had not sent a Terminator to 1995 (leading to the Resistance sending one too) then it's pretty unlikely that Sarah and/or John would have tracked down Dyson prior to Judgment Day and somehow convinced him to help them.