I was pretty critical of the plans for the Botley Rd rebuild, but at least for cycling the results from the first works to be completed seem even worse than I had feared.
The cycle lanes/tracks are too narrow - in places even narrower than the inadequate 1.5m that was promised. This is aggravated by the use of unforgiving full-height kerbing to the carriageway, which prevents easy overtaking and creates a serious hazard if something forces a swerve. The cycle tracks are often directly adjacent to narrow 3 metre motor traffic lanes carrying 30mph traffic — a pedestrian suddenly stepping into the cycle track, debris, or anything else, and someone cycling might be straight under a car or bus. And the cycle tracks lack consistent priority over side entrances and are not flat, going up and down over driveway entrances (where keeping very occasional vehicle movements smooth has been prioritised).
Cycling eastwards here, I would just ignore the cycle provision completely and use the bus lane, which is simpler and more direct, has clearer priority, is smoother and more comfortable, and is safer - with little chance of interactions with pedestrians, kerbs, etc. and with more room to dodge around debris, or just for a safety margin if something unexpected happens. (While I was taking the photos below, two out of five people cycling used the bus lane.) If I were cycling with my 8yo, I'd cycle in the bus lane for the same reasons - there's also enough room there for me to cycle a metre to her right and protect her from overtakes. I would feel pretty bad about doing this in peak hour, since she cycles at about 6mph, but if this were part of our school-run that's what I'd do, given the safety issues. So it's not clear what the use case for the cycle tracks here is: maybe people unwilling to annoy bus and taxi drivers, unaware they're allowed to use bus lanes, or just following the cycle symbols without thinking about it.