I ran it with the same players, but not the same characters. The characters for Dragon Heist were built for a different function (intrigue, social situations) than those for DotMM (dungeon crawl), so it didn't seem logical to connect them. Also, IIRC, I ran DotMM before running Dragon Heist.
Without getting into full Post-Mortem mode on DotMM here, I'd just say that I can't imagine any logical way to connect the two adventures other than the circumstantial location of Waterdeep. But that would be like connecting Rime of the Frostmaiden and Storm King's Thunder just because they're in the North. Even worse, actually, because the two Waterdeep campaigns appeal to widely different playstyles.
Oh yeah. I now remember those being a thing. Couldn't get a single player to even give a second's glance to a solitary faction quest.
Well, for us, we connected with all that Dwarven Ale we found in DotMM, for one. The goblin town with the very smart goblin became a pretty solid contact between our tavern and the underdark, with us hiring the goblins to bring the ale to our tavern, which in turn connected us to becoming a major supplier for dwarven spirits for a while (until they ran out at least). We continuously tried to tell everyone we met to come to our tavern for free drinks.
There's also lots of little side stuff too. The intellect devourers for one.
Granted, the DotMM adventure fizzled unfortunately, due to the group breaking up. I wasn't DMing DotMM, but, I did DM Dragonheist. Not really seeing the wildly different playstyles thing. DotMM is a lot of talking if you don't approach it as a series of combats.
But, yeah, the faction quests bombed for me too. But, again, that was because the group did not care in the slightest about the setting or the NPC's. I would like to run the adventure again, because I do think it has legs, but, unlike the standard dungeon crawls that you typically see in adventures like Storm Kings Thunder or Saltmarsh, it's one that really, really needs player buy in to work.
On a side note about the maps. I understand why WotC uses the Dyson Logos maps. It makes so much sense for a tabletop DM who isn't going to show these beautiful maps to the players, but, rather is most likely just going to sketch out the outlines on a dry erase mat. Heck, even copying and printing the maps would be pretty easy and not too hard on ink once you blew them up to scale. But, as a VTT player, I really don't like them. WotC has used Dyson Logos for a number of adventures now and I hate every single one of them and have to replace every one. It's a huge pain in the ass.