If you use an older edition of Shadowrun, you're running an older edition of Shadowrun, like how people say they run PF2e. Or you saying you'd run Shadowrun Anarchy. But you wouldn't say you're running Shadowrun at a LFG forum and expect nobody to ask or care what edition.
House rules are house rules. They're expected, but usually minor in the scope of the system.
Both are a far cry from "replacing the mechanics entirely". There's only so much you can replace or scrap before you cross a line of it not being the same system anymore, and "replacing the mechanics entirely" definitely crosses that line. It's like when you see someone say "Yeah I'm running D&D5e but I replaced the combat rules and added Draw Steel's negotiation system and reworked all the proficiencies and changed to Vancian spellcasting". At that point, you're basically playing your own system where the stats and classes are inspired by D&D5e, but nobody would call that "D&D5e but with house rules/homebrew". There's more stuff that isn't D&D5e than that is.
This is exactly the kind of thing that people get annoyed at D&D people about, just sort of in reverse; D&D people run different settings with a 5e ruleset and call it a "new system". You're running a system's setting with a different system and calling it "the same system". There's absolutely nothing wrong with pasting Shadowrun's setting onto a new system, but if I run a campaign in Shadowrun's world but I replace the mechanics entirely with D&D5e, I'm not running Shadowrun. I'm running D&D5e.