Is it possible to have a globally unique incremented primary key across all nodes?

[Nandor Krizbai (nandor23)]

As I understand correctly, the bigserial type is unique across all nodes by doing the following:

Citus shifts the start of a bigserial by node_group_id * 2^48, which means that you are limited to a maximum of 2^18 shards that are practically unlimited.

The problem:
I need to produce the shortest possible unique strings in a column, and that's achieved by inserting a row into a table and then taking its primary key and encoding it to produce a string (then updating the desired column with it). Values generated from bigserial would be too big, as the encoded values would be long from the start.

Can the generated ID be unique across all nodes? Even if it's possible, I assume it would be a bottleneck.
Can the bigserial generation be modified so the initial shift would be defined manually?

What are the possible solutions?