Exactly.
Of course they are.
Most of the popular general purpose computing platforms used by consumers allow installation of any app, free from restrictions of the operating system developer. Linux and Windows certainly do. macOS - well, it used to, but Apple have tightened their grip over that more and more lately.
If side-loading is (or includes) the installation of software applications, then yes, it certainly has to do with that.¨
Of course. Most companies active in markets with totalitarian governments do. Just as they did when they removed the VPN apps in China.
Apple's "policy" is also to be a unavoidable middleman for the distribution and installation of applications on their devices. Apple has chosen to assume that position as a gatekeeper - and as such, they "comply with the laws" and orders of government.
Companies (can only) comply with laws and government orders within their "sphere of influence". It's just that Apple has taken the latter, have expanded their iron grip on consumers to almost unprecedented levels in personal computing.
There is no law requiring them to be such gatekeeper. There is no law that saying that the developer of an operating system must control and regulate the installation of applications by its users.
If I were a totalitarian government seeking control of mass communications media (and interpersonal communication), the first thing I would do: Make sure that all applications installable on personal computing devices used by the populace have to be approved - and can be withdrawn on the flick of a switch - by one or a few gatekeepers that "comply with my laws" and orders.