is there a G-N bond in the outside breaker? is the outside breaker the first picture? the wire sizing seems somewhat small to me.
The neutral/ground bars are bonded by virtue of the flat bus bars that connects from the meter box to the bars. Look at the lower-left side of the 1st pic, and you can plainly see the flat bare bus bar feeding up to the first neutral bar, and then the next one feeding across behind the breakers. Service rated only, typical of most meter/panel combo boxes.
That part of the installation is correct.
You can also see that there is an SER cable connected there, complete with a separate insulated neutral conductor, and the bare EGC both connected to the neutral bar.
Seems it would be an easy task to separate the neutrals from the grounds in the larger sub-panel considering both conductors appear to go there.