Connection Pooler string does not honor options parameter with search_path

[abdullahsych]

Bug report

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

Describe the bug

Postgres connection strings support an options query parameter where one can add a specific search_path to be used for the connection:

POSTGRES_CONNECTION_STRING?options=-c%20search_path=custom_schema

This works if I use the direct Postgres connection string shown on the Supabase dashboard but does not work with the connection pooler string (Supavisor). Is this by design? I ran multiple tests and the search path in my connection only updates when I use the direct connection string.

Expected behavior

The search path to be set as specified in the additional parameters passed to the connection pooler string.

Additional context

I am using the connection pooler in Transaction mode.