Ltree extension should be in extension or public schema?

[aishik-pyne]

Bug report

• I confirm this is a bug with Supabase, not with my own application.
• I confirm I have searched the Docs, GitHub Discussions, and Discord.

Describe the bug

I have a list of migrations where in the begining the 1st migration enables all the extensions. Among several extensions I needed ltree extention.
Now unlike other extension where it is supposed to defined in extension schema, there is ambiguity in where tree should be defined.
In my second migration I use create a table using one col being type ltree.

Case 1: Define ltree in extension schema

• supabase db reset works in local db
• supabase db reset --linked fails saying ERROR: type "ltree" does not exist (SQLSTATE 42704)

Case 2: Define ltree in public schema

• supabase db reset fails in local db. At the end there is a 502 code

2025/11/25 19:30:09 HTTP GET: http://127.0.0.1:54321/storage/v1/bucket
Error status 502: An invalid response was received from the upstream server

--debug flag doesn't give much information

Case 3: Define ltree in public and extension schema

• Both local and remote migrations works!
• Remote DB throws a warning saying

Issue
Extension ltree is installed in the public schema. Move it to another schema.

To Reproduce

Steps to reproduce the behavior, please provide code snippets or a repository:

1. Create 1st migration file:

create extension if not exists "ltree"
with
  schema "extensions"; // Or use `public` to test out the other case

2. Create 2nd migration file:

create table product_taxonomy.categories (
  id text not null,
  locale text not null, 
  version text not null, 
  name text not null, 
  parent_id text,
  tree_path ltree not null, -- hierarchical path (hyphens converted to underscores)
  level integer not null default 0, -- depth in hierarchy (0 = root)
  breadcrumb text not null,
  primary key (id, locale, version),
  -- Self-referential FK ensuring parent exists in same locale & version
  foreign key (parent_id, locale, version) references product_taxonomy.categories (id, locale, version) on delete cascade
);

Expected behavior

Ideally the docs should mention which schema to keep ltree extension in.

Screenshots

NaN

System information

• OS: macOs
• Supabase CLI Version: 2.62.5

Additional context

Add any other context about the problem here.