Just want to confirm for clarity, that there is no breaker / disconnecting means between this panel and the meter base? Per code, bonding is to take place at the first point of disconnect of source, and not to be bonded past.
Provided that the meter feeds directly into the panel and that the main breaker for that panel is the first point of disconnect for the meter, yes, the neutral shall be bonded to ground in the panel and the grounds and neutrals can be bonded within that panel as they are.
It appears, based on your pictures that the grounds are bonded with the neutral at the panel by landing the grounded electrode conductor and equipment grounding conductors to the neutral bus, but that the can / enclosure itself and the small grounding bar to the left is NOT bonded and does not have a solid path to ground. Based on your picture, if you look on the top right corner of the neutral bus, you will see a roughly 1/4" hole, which is where a bonding screw is installed to bond the neutral bus to the enclosure.
I would suggest taking a multimeter and testing for continuity between the neutral bus and the grounding bar in the lower left corner to see if there is in fact a solid bond.
I have seen a fair amount of people land grounds to the neutral bus at the first point of disconnect / main panel, like has been done in the pictures in your post, but if the bonding screw is not installed, future people may assume that the enclosure itself is bonded and make ground connections via added grounding bars to the enclosure, assuming that the enclosure is grounded. In general, I hate this way of panel makeup, because most often it opens doors for future problems to be created by less experienced individuals, and creates a LOT of unnecessary work if that panel were to ever become something other than the main disconnect, in which case all the grounds would need to be separated from the neutral and landed to a grounding bar.
As I have explained it to early apprentices in the past... just because it works and provides the correct path DOESN'T make it right! Plan for future changes by doing it RIGHT the first time and always land your grounds to a properly sized ground bar and your neutrals to the neutral bar... EVEN IF the two are bonded internally... it just makes it easier for the next person who has to work on it... and I always remind others "just remember... that next person that has to work on this just might be YOU!"
Just my two cents.