s_contact_phone field is not in t_item table
so the database has not been updated

Where is the error log located? Do I need to enable debugging in config.php file?

It is good to enable error logs.
Error log is usually located in folder defined by your hosting

I have all apache/db/php error logs enabled on the server but there is absolutely nothing related to osclass update issue I mentioned.

On the front office the console shows two errors:
tipped.js error (illegal character 10:548)
tipped is not defined /oc-content/plugins/osclass_pay/js/user.js?v=20200920171156:288

but this shouldn't affect the database to be updated during osclass upgrade...
issue remains unsolved

It could, as that update is ajax based.
Try to disable osclass pay plugin and try again.

Yes, it could and that was the problem.
After I deleted pay plugin the database update works and a new fields has been added now.
Only one minor issue is the warning as the release.notes.php does not exist in the package.

Warning: include(): Failed opening '/public_html/oc-includes/osclass/assets/release.notes.php' for inclusion (include_path='.:/usr/share/php') in /public_html/oc-admin/themes/omega/tools/version.php on line 29

When you got that?

After clicking the UPDATE NOW button during 3.9 -> 4.0 db update on the back office.
I assume the missing file should be in OMEGA theme. It is included at the end of the update to display some comments about a new version etc.

include osc_lib_path()."osclass/assets/release.notes.php";

It is not theme file, it is from core. Maybe its location has changed, will check it out.

@piter
Problem found and fixed, will be updated in v4.0.1
Thanks for feedback 

I just updated to version 4.0 on locally installed osclass with xampp and it seems to work perfectly!