Are university professors allowed to use any computer they want for work? Do universities restrict the brand or manufacturer of computers their professors are allowed to use for work?
May a PhD advisor ban certain computer brands?
Are there any restrictions on using your own funding to buy certain brands of computers?
Corporate restricts company computers allowed for security reasons but the university doesn’t technically own any of the professors work or consider it their proprietary knowledge so are they allowed the control the electronic storage system of it?
University purchasing systems are very complicated and they are all different.  It is common for universities to make a contract with a supplier stating that they will use that supplier exclusively in exchange for a discount.  Often there will be loopholes.
Your supervisor can certainly refuse to purchase certain brands with funds the supervisor controls.
If you have a grant, you will be required to follow the university's purchasing policies.
Traditionally, most universities allow faculty and students to do their work using personal computers of any type.  However, this could be limited for confidential information.  There are laws limiting the use of educational and medical information which vary from place to place, and there are also policies.