Paul W.S. Anderson confirmed that it's connected on Soldier's commentary. Considering that David Peoples called it a spin-off originally but then said that it was actually not that and came as a response from Terminator, I think this:
1. Soldier was written as an original idea, separate from Blade Runner to begin with. Peoples never saw the finished film though and he's talking about when he originally wrote up the story for Soldier in 1984, literally 14 years before the film actually came out.
No, I never had any thoughts about that... I wrote Soldier in 1984. Very quickly on my own. I wrote it because I saw the first Terminator in the theater, stunned. And it was such a wonderful movie. I'd always wanted to write a movie in which there was a tough guy who would be seemingly unsympathetic in the lead, and I felt that The Terminator was almost there. Later in the sequel, it was determined he was the hero, but at the time, he was sort of a villain. But the fact is, he was so great. I went off, and I decided to write about this soldier."
2. Soldier became a spin-off down the line for both David Peoples and the director. Quoting Anderson:
"Now, on Kurt's shoulder there is the Tanhauser Gate. That's one of the battles that he fought in, which people might recognise from Blade Runner as well, Rutger Hauer talks about C-beams glittering in the darkness off the Tanhauser Gate, and David Peoples also did the adaptation of Blade Runner. There's a lot of references to Blade Runner in this film. I always saw the two movies, Soldier and Blade Runner, although they're very, very different, as existing in the same universe, so that if Kurt ever went to Earth, he'd encounter Harrison Ford down there."
"So, yeah. Blade Runner was a constant influence to us during the making of this film. And also thematically, Blade Runner is very much about the machine that becomes as human as it possibly can be, Rutger Hauer's character, whereas this movie is about the man who becomes as machine-like as the military can make him. So in a way, both Kurt and Rutger are looking for their humanity."
3. Both films are owned by Warner Brothers.
4. The film contained the implication of replicant soldiers replacing Todd.
5. A police spinner from Blade Runner appears.
6. The wars from Blade Runner are shown on computer screens, tattooed on Todd's arm and the Tanhauser Gate conflict is mentioned in dialogue.
7. 2036: Nexus Dawn, purposefully or not, sets up the events of Soldier.
8. The references to Blade Runner and Soldier in Aliens: What If...? were confirmed to be because the writers considered it the same universe as Alien during a podcast with AVP Galaxy. (Less relevant but still, it places Blade Runner and Soldier together)