GENERATED STORED columns and table rewrites?

Hello,

Does adding a GENERATED STORED column need to rewrite the table (like
adding a column with a DEFAULT before 11)? Neither the ALTER TABLE docs [1]
nor the generated column docs [2] discuss this. The former has a very nice
Tip regarding DEFAULT columns--maybe we should clarify GENERATED STORED
behavior either way? It seems like a very similar issue. Experimenting with
this, \timing suggests that there is work proportional to the size of the
table, but I'd like to understand the behavior better (and other users
probably would, too).

Thanks,
Maciek

[1]:
https://www.postgresql.org/docs/current/ddl-alter.html#DDL-ALTER-ADDING-A-COLUMN
[2]: https://www.postgresql.org/docs/current/ddl-generated-columns.html