I'm obsessed with my Detroit: Become Human themed save since fall 2018. Although it has evolved a lot since then, the core is still there.
Do you go all-out and make all the worlds themed - buildings, the sims, mod out phones etc if needed? Do you just stick to doing one world? Or do you just plop in one household of characters amongst all the 'normal' sims? (And, if you do that, do you make that one house themed?)
Characters? Definitely all out, but I didn't start that way. It was a slow process that started with the wish to give a single minor character, Daniel Phillips, a better ending. My other sims were to be OCs that fit the Detroit in 2038 setting.
Over time I added more and more characters from the Detroit game, first the cops, then Daniel's old family, until by now I have the most obscure Detroit characters running around and hardly play my OCs anymore. Out of my 200 favorited sims I play five households regularly, and others sporadically. These regulars are all Detroit canon characters.
Since they are an importent part of the Detroit lore, I heavily curate my police co-workers. Anybody who isn't a sim from DBH (or from the first batch of game-generated co-workers from 2018) gets deleted right on spawning. Career levels are fixed (with some wiggle room).
Buildings, nah. I grabbed what I could find in the gallery. The most I did was re-painting the walls of the ingame police station to reflect the color scheme of the Detroit Police Department. I also added a rooftop farm and an android store, but they look nothing like the originals.
How do you cope with modern items if your game is set in a different era (such as background buildings and cars)?
I usually don't have that problem, more like the opposite. The save being set in the near future, I can allow objects I wouldn't normally, like the infamous rocketship in the backyard, or use genetic engineering as an excuse to include mermaids and fantasy cc for pets.
For the longest time vampires were posing a problem, because the supernatural doesn't exist in the dbh setting. I retconned the vampires to burglars (if they broke in) or malfunctioning androids (if they visibly smoked in public). By now that has changed, the save now has lore to accommodate all packs.
Do you try and play out the characters as per their book/film (maybe even trying to get the correct gender of any kids if they have them) or do you play them however the game takes them?
The game certainly gets to make suggestions, but when in doubt I go with what feels the most in-character. When former enemies organically grow closer over a long time or when someone picks up an instrument, that's okay. But for romances I stick to my headcanons, regardless of where the game tries to send the sims. Shippers gonna ship, I guess...
One especially out of the left field development was when Daniel got the "Know your universities" notification. I interpreted that as the government offering him a scholarship and he chose to major in Psychology. Daniel now works as a teacher, what I think fits him, but without the game giving me that nudge I wouldn't have considered that career path.