The HDW-F900 was produced with a maximum resolution of 1080i upto 2003, at which point an upgrade package was released which allows the camera to record 1080p at 30, 24 & 23.98 (a model that integrated this upgrade was released in 2006), but the tape that was used, HDCAM, could only store up to 1080i natively, with 1080p being stored in segmented sections. (HDCAM SR can store native 1080p, but according to all the sources this format was not used, except maybe in the editing bays.).
Plus many NLE editing suites at the time allowed for interlaced footage to be interpreted into progressive video.
Therefore, especially with the 1080p only being available via an upgrade (and even to rent it probably upped the cost tremendously) at the time of Enterprise, and with the tape format only being able to natively support 1080i, it is most likely that Enterprise Season 4 was shot in 1080i.
(Also I just watched Mirror part 1 where they shot on film and tape for the episode, and the main episode looks softer than the teaser. If you look at the people's outlines, the people in the teaser have sharper outlines, but then after the opening the outlines are soft.)