i took a break from DS3 bc i had played thru it so many times i was in danger of boring myself plus a friend found a PS3 at a thrift store w MGS4 for $60. he already had one so i gladly took it off his hands and walked down to Gamestop in the pouring rain the next day to buy Demon's Souls.
DeS is so good and coming from Dark Souls 3 feels very natural! the levels are very linear like DS3 and there are a good 3-4 areas that are either direct remakes of DeS areas or highly referenced in DS3. warning -- some DeS/DS3 spoilers here!
it is funny bc i have seen DS3 get so much flak for ripping of DS1, yet it is clearly trying to reference the first game, which was largely ripped off by DS1. the gargoyles taking you somewhere? DeS. the fire breathing dragon bridges? DeS. Patches the thief who tries to kill you in every Souls game? DeS. i had thought the laughing inquisition-goth Evangelists were a Bloodborne reference: nope, turns out they are in DeS! also squid-face Cthulu wizards!
Irithyll Dungeon and Firelink Shrine are the most famous references in DS3, being full remakes of the Tower of Latria and Nexus in DeS. the High Wall and Lothric Castle itself are both very reminiscent of DeS's Boletaria, featuring the same red-eyed knights and even some of the same enemy movesets and models. then there is the Stormruler you use to take down Yhorm the Giant - this is a special weapon used in DeS at the coolest end-game soul farming spot ever in a videogame. the whole Shrine of Storms area has that windswept-rocky-cliffside-ruins feel that opens up DS3 just outside Firelink Shrine and again later in Archdragon Peak. parts of DeS's Shrine of Storms feel like the area in DS3's Cruxifiction Woods, the ruins before you fight the Crystal Sage. and this is just level design, there are character designs, lore concepts, weapons, armors, etc. it is shocking to me just how much of the Dark Souls series was baked into DeS. and it isn't even rough and sketchy - DeS was a polished product.
anyways just wanted to rant a little. highly recommend DeS for any fans of DS3. it is the Souls games closest to it. imo DS3 was designed to be an homage to the entire series in this way, starting and focusing mostly on DeS. the number of references to DS1 are far fewer than the references to DeS. with DS3 they are thematically and gameplay wise bringing it back home, back to where it started: linear and tightly designed levels packed with atmospheric detail. i wouldn't be surprised if there was lore theories about the series looping in on itself tbh.