The Empire's claim to meritocracy seems to... vary.

van Baelsar seems to have been a firm believer in the concept, though that doesn't seem to be the case for most other Imperials we've met. Rhitahtyn and Fordola both got their high rankings under his command, and he even accuses the soldiers of abandoning Rhitahtyn to his death at Cape Westwind (untrue - Rhitahtyn told them to leave so we wouldn't kill them in the battle). Varis also promoted van Hydrus on merit, though this could be seen as blending with nepotism a bit (van Hydrus helped Varis become Emperor, which he rewarded by giving him the rank of Legatus... if I remember correctly).

On the other hand, the racism coming from nearly every other Imperial is blatant. This is probably hammered home best with both mal Asina's declaration that the Garleans are superior, both physically and intellectually (except their inability to wield magicks), and Fordola's painful acknowledgement that you won't be treated as an equal unless you prove yourself to be exceptionally superior to Garleans. (There's even a bit of sexism there too, with Imperial soldiers implying Fordola only got her rank by whoring herself out, rather than because she deserved it.) This could be seen as purely due to Zenos' malign influence, but even van Hydrus repeatedly refers to the Eorzeans he interacts with as savages... so it's not quite so contained.

If memory serves right the "sas" limitation only applies to naturalized citizens - those born into the Empire can (theoretically) go as far as their merit takes them (up to "van," but "wir / yae / zos" is still reserved for the royal family), but integrated peoples can't advance further. My memory might not be right, though, and if it's wrong that is literally institutionalized racism.

Class divides, even among Garleans, are also there. Again, shaky memory, but I believe it was mentioned that van Hydrus came from common birth, which is why so many of the other Imperial Legatuses (nobles) were opposed to his promotion and why there were efforts to sabotage his mission on Azys Lla that led to Sophia's release.

... while the Empire says it's meritocratic, that's not necessarily true. What things say on paper and how they work in practice are often two different things.