I had understood that Aurora mainly differed with its lower level internals implementation, but that it should look the same from a user perspective and thus be drop-in compatible with regular Postgres in practice, such that any database schemas or clients that work in regular should work with it unmodified.
What are the main differences you see in Aurora that are surfaced to users such that they would have any kinds of impact on pgAdmin compatibility?
Things related to the underlying storage engine like system columns on tables, for example xmin/xmax/ctid which might be different, but there are also a bunch of unsupported features (https://docs.aws.amazon.com/aurora-dsql/latest/userguide/working-with-postgresql-compatibility-unsupported-features.html), none of which pgAdmin knows are unsupported or in what way - e.g. are there system catalogues that are missing, will DDL be accepted but do nothing or will it throw errors, will some of the catalogues be missing individual columns that may not be needed because certain features are unsupported? The list is likely longer than that, but you get the gist.