Why are global temporary tables truncated when the connection is closed

One way to do this would be Object Types, in this case the type would be analagous to your #t1. So it would need to be defined somewhere but it would not need to be global, it could be per-schema or per-procedure even. First, we can create a type:

SQL> create or replace type t1_type as object (x int, y int, z int)
  2  /

Type created.

SQL> create or replace type t1 as table of t1_type
  2  /

Type created.

Now set up some sample data:

SQL> create table xy (x int, y int)
  2  /

Table created.

SQL> insert into xy values (1, 2)
  2  /

1 row created.

SQL> insert into xy values (3, 4)
  2  /

1 row created.

SQL> commit
  2  /

Commit complete.

And create a function over this data returning our "temporary" type:

SQL> create or replace function fn_t1 return t1 as
  2  v_t1 t1 := t1();       -- empty temporary table (really an array)
  3  v_ix number default 0; -- array index
  4  begin
  5  for r in (select * from xy) loop
  6  v_ix := v_ix + 1;
  7  v_t1.extend;
  8  v_t1(v_ix) := t1_type(r.x, r.y, (r.x + r.y));
  9  end loop;
 10  return v_t1;
 11  end;
 12  /

Function created.

And finally:

SQL> select * from the (select cast (fn_t1 as t1) from dual)
  2  /

         X          Y          Z
---------- ---------- ----------
         1          2          3
         3          4          7

As you can see this is pretty clunky (and uses collection pseudo-functions, which is an obscure feature at the best of times!), as I always say, porting from DB to DB is not merely about syntax and keywords in their SQL dialects, the real difficulty comes in different underlying assumptions (in the case of SQL Server, that cursors are expensive and their use avoided/worked around at all costs).

There is an exception. When you define a before insert, row-level trigger on a table and issue a single row INSERT statement, the table is mutating error will not be raised. But if you define the same kind of trigger and issue a multi-row INSERT statement, the error will be raised. Here is an example:

SQL> create table TB_TR_TEST(
  2    col1 number,
  3    col2 number
  4  )
  5  ;

Table created

SQL> create or replace trigger TR_TB_TR_TEST
  2  before insert on TB_TR_TEST
  3  for each row
  4  begin
  5    SELECT max(col1) + 1 INTO :NEW.col1
  6      FROM TB_TR_TEST;
  7    UPDATE TB_TR_TEST SET col2 = 5000;
  8  end;
  9  /

Trigger created

Here is a single-row insert statement, which won't raise mutating table error:

SQL> insert into TB_TR_TEST(col1, col2) values(1,2);

1 row inserted

SQL> insert into TB_TR_TEST(col1, col2) values(3,5);

1 row inserted

SQL> commit;

Commit complete

Here is a multi-row insert statement, which will raise mutating table error:

SQL> insert into TB_TR_TEST(col1, col2)
  2    select 1, 2
  3      from dual;

insert into TB_TR_TEST(col1, col2)
  select 1, 2
    from dual

ORA-04091: table HR.TB_TR_TEST is mutating, trigger/function may not see it
ORA-06512: at "HR.TR_TB_TR_TEST", line 2
ORA-04088: error during execution of trigger 'HR.TR_TB_TR_TEST'