How to split a terraform file (main.tf) in several files (No Modules)?
You can try as per https://marcelzehner.ch/2018/05/22/terraform-using-multiple-files-for-configurations-and-variables. I'm sure it will be useful in your scenario.
Even though no module has been included in your project. Terraform always runs in the context of a single root module. The .tf file is under root module.
Based on Terraform Documentation:
Terraform evaluates all of the configuration files in a module, effectively treating the entire module as a single document. Separating various blocks into different files is purely for the convenience of readers and maintainers, and has no effect on the module's behavior.
https://www.terraform.io/docs/language/files/index.html#directories-and-modules
Terraform does not ascribe any special meaning to which filenames you use and how many files you have. Terraform instead reads all of the .tf files and considers their contents together.
Therefore you can freely move the blocks from your main.tf file into as many separate .tf files in the same directory as you like, and Terraform will consider the configuration to be exactly equivalent as long as you change nothing in the contents of those blocks while you do it.
(There is a special case for Override Files that makes the above not strictly true. As long as you avoid naming any of your files override.tf or with an _override.tf suffix that special case will not apply, but I'm mentioning it just for completeness.)
The command terraform apply can be apply to a file or a directory, according with the documentation. Thus, put all your file in a directory and apply them.
The tfstate file is relative to a deployment. You will have only one.
About the lowest impact... Hard to say. All depends of your variables and your resource dependencies. If you have to search is several file to understand how a resource is created or where a variable is set, multiple file isn't a great idea... However, it's your customer requirement and do it the much simpler for readability.