That's a very common issue with Nissans around that year. My 2000 Xterra does the same thing, Xterras and Frontiers that have come through my family's shop do the same thing, and even my buddy's 1994 Nissan Hardbody pickup did this before he sold it. From my experience and what my father has told me, the issue usually doesn't indicate a failing transmission unless it never engages the forward gears. Cold weather also makes going into drive take far longer.

I don't know what sensor you're referring to but try putting a bottle of Lucas transmission additive, the stop slip stuff, in with you transmission fluid. It makes a very noticeable difference, but doesn't eliminate the delay when shifting to D.

Lucas transmission fix - O'Reilly's (Mar 2022)

 

Be really careful about what kinds of stop-leak stuff you put in any automatic transmission. If it has stuff in there to swell the seals, they usually harden not too long after that and then they leak even worse.

Parts wear out, and if it's slipping, you might get a few more miles out of it from a bottle, but you'll still need to do the work to repair or replace the worn parts.

I've used the Lucas Power Steering fluid with conditioners and it has made the PS pump in my 2011 Chevy car a lot quieter, especially when making a U-turn at more than 5 mph, when the stock fluid would groan a lot.

I use in my Xterra as well.

So Lucas probably makes good stuff, but you still need to read the label and know what's inside.