Consider below
create temp function  extract_keys(input string) returns array<string> language js as """
  return Object.keys(JSON.parse(input));
  """;
create temp function  extract_values(input string) returns array<string> language js as """
  return Object.values(JSON.parse(input));
  """;
create temp function extract_all_leaves(input string) returns string language js as '''
  function flattenObj(obj, parent = '', res = {}){
    for(let key in obj){
        let propName = parent ? parent + '.' + key : key;
        if(typeof obj[key] == 'object'){
            flattenObj(obj[key], propName, res);
        } else {
            res[propName] = obj[key];
        }
    }
    return JSON.stringify(res);
  }
  return flattenObj(JSON.parse(input));
''';
create temp table flatten_table as 
  select json, offset, key, value
  from your_table, 
  unnest([struct(extract_all_leaves(json) as kv)]),
  unnest(extract_keys(kv)) as key with offset
  join unnest(extract_values(kv)) as value with offset
  using(offset);
execute immediate (select '''
  select * except(json) from (select * except(offset) from flatten_table)
  pivot (any_value(value) for replace(key, '.', '_') in (''' || keys_list || '''
  ))'''
from (select string_agg('"' || replace(key, '.', '_') || '"', ',' order by offset) keys_list from (
  select key, min(offset) as offset from flatten_table group by key
))
);            
if applied to sample data as in your question
create temp table your_table as (
  select '''{
    "key1": {"key1.1":"val11", "key1.2":"val12"}, 
    "key2": {"key2.1":"val21", "key2.2":"val22"}
  }''' json
);            
output is
