What is the Postgres's equivalent/closest lock of Microsoft SQL Server's IX (Intent Exclusive) lock?
You need to take a step back and check what Intent Locks are made for.
Transaction locking for MS-SQL server is broadly explained here:
https://docs.microsoft.com/en-us/sql/relational-databases/sql-server-transaction-locking-and-row-versioning-guide
And for PostgreSQL it's broadly explained here
https://www.postgresql.org/docs/current/mvcc.html
MS-SQL server doc says:

Intent locks are named intent locks because they are acquired before a
lock at the lower level, and therefore signal intent to place locks at
a lower level.
Intent locks serve two purposes:
To prevent other transactions from modifying the higher-level resource in a way that would invalidate the lock at the lower level.
To improve the efficiency of the SQL Server Database Engine in detecting lock conflicts at the higher level of granularity.

There is no equivalent to intent locks in PostgreSQL. The IS, IX, SIX, IU, SIU, UIX lock modes have no equivalent because they refer to a concept that PostgreSQL doesn't have and seemingly doesn't need.