Does MacStudio M4 Max and Mac Mini M4 Pro works with any keyboard - monitor - mouse ?

The last word on your question. There are innumerable Macs users using third-party keyboards, mice and monitors.

FWIW, I am currently using a $8.99 (US) Belkin wired 3 button mouse on my M3 iMac running Sequoia 15.4. I also tested a Bluetooth Compact Backlit keyboard from Matias, it also works fine.

I have a Mac Studio at my workplace.

It is connected to a lowly VGA monitor (using a USB-C to VGA adapter), and for a time I use old "pc" USB keyboard and mouse. I now got an Apple keyboard (loan from a friend) but could have continued with the clunky keyboard. The mouse is still that old pc one.

It works.

Certainly most will.

You certainly don't need a Magic Mouse and Keyboard. There are many Mac compatibles from Logitech, Matias, Satechi, MacAlly, etc. As far as monitors, I don't know of any that won't work.

This is a Loaded question that is doomed for failure

Any of the afore mentioned Apple Computers should work with Apple Displays and work with any Apple Keyboard or Apple Mouse

The caveat being Apple Computers and Apple Accessories

It is when a user introduces Third Party Devices / Accessories that things get cloudy

Some Third Party Devices / Accessories may function and some may not perform to the Exceptions of the user

As for Proof ?

Apple Designed and Built the computer to Apple's Specifications

Apple Designed and Built the Apple Displays, Keyboards and Mice also to Apple's Specifications

Apple Designed and Built the Operating System with the idea in mind that one would use their Accessories / Displays

In summation

Certain misconceptions persist regarding the relationship between Apple Computer and third-party devices, applications, extensions, services, and accessories.

These misconceptions often arise when third-party products fail to function or meet user expectations.

Apple is responsible for addressing issues with its own services, applications, operating systems, and accessories.

However, Apple cannot rectify user choices of third-party products  installed and used on their computers.

This responsibility lies solely with the third party to evaluate the performance of their products when used on an Apple Computer running the intended version of macOS.

to use the analogy.

A High Octane Vehicle designed to use High Octane fuel for peak performance can use a lower octane fuel, but it won’t reach its full potential. 

Indeed. Even a $20 Logitech Windows keyboard works for the most part, except the functions printed on the function keys on an Apple keyboard. And the Windows key is the Command key.