I don't really know what I am talking about, But I thought that postgres function volatility was introduced for this exact reason, that is, As a clue to the optimizer where it can and cannot push stuff down.

https://www.postgresql.org/docs/15/xfunc-volatility.html

I do note that the postgres explain appears to keep the join filter on the top level.

  explain select count(*) from
   generate_series(0,999) a
     inner join
   generate_series(0,999)
     on random() < 0.5
  ;
                                      QUERY PLAN                                      
  --------------------------------------------------------------------------------------
   Aggregate  (cost=25843.34..25843.35 rows=1 width=8)
     ->  Nested Loop  (cost=0.01..25010.01 rows=333333 width=0)
          Join Filter: (random() < '0.5'::double precision)
          ->  Function Scan on generate_series a  (cost=0.00..10.00 rows=1000 width=0)
         ->  Function Scan on generate_series  (cost=0.00..10.00 rows=1000 width=0)