Guess: Junctions are weighted.

There's an extra junction on the green route. Junctions often add delays when giving way to traffic, so the algorithm may choose routes with fewer.

I'd say it depends on the heuristic of the path planning algorithm, eg. if road surface is taken into account and the road it chose is asphalt while the other one is dirt then that path makes sense.

What application are you using to find this path? OSM in itself doesn't do path planning if I'm not wrong, it's just the map's structured data

So, two things are to consider here:

1. Is the underlying OSM mapping data correct? This is something we can not deduct from the screenshot. If it is not to privacy violating you might share the exact location.
2. Is the routing algorithm working correctly? Once we made sure that the underlying data is correct, we can see, if it is working. Then we could file a bug report if still something is off.

It always takes a few minutes for the map to render the updates (and often requires you to clear the cache: on the browser at least). For the routing to take the new path into consideration, it usually takes about a day or something, so I wouldn't be waiting for that; just try again tomorrow and it should work. ;)

Left turns may have a higher cost for routing than right turns because of turn on red laws.

As for the actual question at hand: don't rely too much on OSRM. It's just the "default" router, and there are many others out there. E.g. both Valhalla and Graphhopper suggest the shorter route in pedestrian mode.

Also, will OSM - OrganicMaps\CoMaps will introduce any time soon ability for public transport routes?

I don't think there are any current plans for it. It's actually really difficult to get right.

OsmAnd kinda cheats and doesn't have any scheduling information, basically it assumes that the transit comes often enough that it doesn't matter, which is fine in bigger cities. However, if your bus comes only twice a day it will be an issue.

There's an open-source app for public transit called Bimba. It is a bit janky, and it requires you to be online for proper routing, but it does work for many cities. It still needs a lot of polishing before I'd consider it done, and actually I'd love for it to just become an OsmAnd plugin at some point.

I would not wanna turn left on what may be a blind intersection. If that parallel road you're turning left on is 4 lanes of traffic I'm taking easier right of way.

Edit: also if your destination is immediately across from a 3 way its safest to turn left into it as opposed to crossing two right of ways

Which direction is the path? If it's marked as a one-way road, it may not consider it. Or, as somebody else pointed out, the routing application might not have the up to date map. Give it a day or so.