Hi,
Thanks for the very detailed report, it made this quick to pin down. You found a real bug in HikaShop and it is directly linked to the Joomla 3 to Joomla 5 migration. I reproduced it here with a field named e_CopyMinderKey and I've fixed it.
The cause is the capital letters in the field name key. When HikaShop prepares the data of a record before writing it, it normalizes the column names to lower case, so e_CopyMinderKey is passed as e_copyminderkey. Under Joomla 3 that made no difference, since MySQL column names are not case sensitive. But since Joomla 4, Joomla's updateObject() compares the name you give it with the columns of the table letter for letter, and silently drops anything that doesn't match exactly. So the column is simply left out of the UPDATE query: no error, "Successfully Saved", and the value still NULL. That is why it started the day you migrated.
To answer your questions:
1. Yes, now confirmed, and it affects any custom field with an uppercase letter in its name key, on the user, address, order and product tables alike.
2. They are supported again with this fix. HikaShop has been forcing new field name keys to lower case for years, which is why only fields created on your old installation are affected.
3. No migration or resave is needed. Note that creating a new record was already saving these fields correctly, it is only the update of an existing record that was losing them.
4. It was in checkFields() in administrator/components/com_hikashop/classes/field.php, at the line that lowercases the column name.
5. No, your view overrides are not involved here. Just download the install package of the latest version of HikaShop on our website and install it on yours and you'll get the patch for this.