Assuming you want to get up to 30 characters on each line (rather than fixed 30 character offsets from the first character), here's one way to do it:

- Split the string into a row per word
- Place these in groups up to 30 characters long
- Use listagg to combine the strings back together

You can use your favourite CSV-to-rows trick for the first part, swapping commas for spaces. For example:

with vals as (
  select 'Split a new line after 30 character' str 
  from   dual
), rws as (
  select regexp_substr ( str, '[^ ]+', 1, rn ) substr, str, rn
  from   vals, lateral (
    select level rn from dual
    connect by level <= length ( str ) - length ( replace ( str, ' ' ) ) + 1
  )
) 

You can then use match_recognize to split these into groups up to 30 character long, using a similar method as described by Keith Laker:

https://blogs.oracle.com/datawarehousing/post/managing-overflows-in-listagg

The final step is to listagg the strings back together, grouped by the original string and the group calculated above

Giving:

with vals as (
  select 'Split a new line after 30 character' str 
  from   dual
), rws as (
  select regexp_substr ( str, '[^ ]+', 1, rn ) substr, str, rn
  from   vals, lateral (
    select level rn from dual
    connect by level <= length ( str ) - length ( replace ( str, ' ' ) ) + 1
  )
) 
  select listagg ( 
           substr, ' ' 
         ) within group ( 
           order by rn 
         ) split_str
  from   rws match_recognize (
    partition by str
    order by rn
    measures 
      match_number() as grp,
      length ( init.substr ) + sum ( length ( thirty.substr ) ) as l
    all rows per match
    pattern ( init thirty* )
    define
      thirty as length ( init.substr ) + sum ( length ( thirty.substr ) + 1 ) <= 30
  )
  group  by str, grp;
  
SPLIT_STR                   
Split a new line after 30    
character 

Note that this assumes all words are only separated by single spaces. Real-world text is often messier than this, with splits on carriage returns, punctuation, etc. In general this is a hard problem to solve!