BUG: to_string truncation row with index=False
- [x] closes #40904 
- [x] tests added / passed
- [x] Ensure all linting tests pass, see [here](https://pandas.pydata.org/pandas-docs/dev/development/contributing.html#code-standards) for how to run them
- [x] whatsnew entry
  - Already have one for the same bug, not sure if I need one for this.

lgtm. if @pandas-dev/pandas-core or @pandas-dev/pandas-triage can have a look to double check. I checked how ``to_string`` looks on this branch.
I confirm that the new behavior is favorable. @jreback @ivanov Is the PR ready for merge? I don't see the option to complete it from my side. > ...@ivanov Is the PR ready for merge? I don't see the option to complete it from my side.

I think you meant to tag @ivanovmg  thanks @mikeronayne 