When Windows 10 batch renames files it uses a format like: "file (1).html".
Is it possible to set the the default for batch renaming to format the files like: "file1.html" to avoid additional characters instead?
Not from Windows Explorer. You'd want to use PowerShell or a third party program, many of which are free. Batch renaming is pretty common, so there are plenty of choices. There isn't a way to change the format for the Windows Explorer way of doing things, though.
If you are not comfortable with PowerShell and don't want to download a virus or malware, then I'll go ahead and recommend Irfanview. It's very popular image modification software and it happens to include batch renaming in its functionality (File -> Batch Conversion/Rename). In there, you can specify the exact format you want for the renamed files. And, IrfanView (As well as its plug-ins if you decide you like the image editing part of the software) is 100% free.