[2020] Old save = slower game?

The older save will likely also see some worse performance as you have more of a city built there. As the city grows, the game slows down because there are more citizens to simulate. So a new city which is smaller would run more smooth.

Adding DLCs is pretty painless. The changes come with the free patch, that comes when a DLC releases, so once you're passed that, getting the DLC doesn't really matter. Ofc building stuff with a new DLC might disrupt your city - building a large new industrial area with Industries can affect your old zoned industry for example - but nothing that isn't solveable. :)

If we're talking same city (so same amount of agents simulated and same buildings/trees/props), then it should perform the same. Being older shouldn't have any effect on performance.

There might be some difference in the case of a modded save. Say if the old city was made using some mod(s) that have since broken and have been removed. The changes the mod(s) made to the savefile would still be in the save, which could affect performance, compared to a new version of the exact same city, which never had the old mod(s). But that's just hypothetical as I'm not even sure if any mods exist, which would apply. :P