What's it called when a company owns products or services that strictly limit consumers to that company's products or services?

Proprietary

'Proprietary systems' or products, limit you to the use of the offerings being created by the 'proprietor' or owner of the company.

For example:

• only proprietary ink cartridges can be used on Epsom printers.

• Apple systems apps are proprietary - they can't be used on other systems

Definition, Merriam-Webster

Definition of proprietary (Entry 1 of 2) 1: one that possesses, owns, or holds exclusive right to something specifically : PROPRIETOR sense 1 2: something that is used, produced, or marketed under exclusive legal right of the inventor or maker

vertical integration

Vertical integration is the combination in one company of two or more stages of production normally operated by separate companies. For example, if I manufacture Widgets and these Widgets are made out of wood, to vertically integrate, I might buy a lumber mill or even forests, and I might also open my own Widget stores so that the only place anyone can buy a Widget is at my Widget store.

Complete vertical integration means one company controls the end product as well as all of its component parts, so the company needs to buy nothing from anyone else but rather owns and operates every aspect of production of everything that goes into that product from raw materials through bringing it to selling it to consumers.

EXAMPLE:

A quintessential example of a company that completely vertically integrates is Apple, Apple being both famous and infamous for its iron grip on control over every single aspect of its products, from accessories, to software, to literally everything. The first Macintosh computers, for example, were sold as a single unit and couldn't even be cracked open. Everything contained in them and any and all periphery items were completely proprietary, a business model that Apple founder Steve Jobs vehemently insisted on and fought tenaciously to keep, even against his own shareholders, and which in the end proved to be prescient and wise and why Apple still completely vertically integrates even though Steve Jobs has been gone now for years, having died in 2011.

A counterpoint to Apple's total vertical integration is IBM, which did very little to vertically integrate and even made its operating system opensource, resulting in IBM's hardware being undercut in the marketplace by off-brand clones dubbed IBM compatible PCs and by IBM's operating system and application software ultimately being supplanted by competitors, chiefly Microsoft, thus IBM is now no longer the chief manufacturer of hardware or software for what was initially its product: the PC.

Through extremely tenacious and even litigious vertical integration, Apple has quite effectively avoided the pitfalls that cost IBM nearly all of its market share in every aspect of the PC, IBM's original invention and brainchild, by aggressively maintaining tight control of every aspect of its products.

I think the phrase that best describes it in tech is a closed ecosystem, although that might apply to a group of products or an operating system rather than a single product.

A popular but less precise alternative to “vertical integration” from @BenjaminHarman, often applied to Apple®, is:

walled garden

The literal definition of this is horticultural. The Wikipedia entry has:

A walled garden is a garden enclosed by high walls for horticultural rather than security purposes, although originally all gardens may have been enclosed for protection from animal or human intruders.

In this sense it is a positive description — the walls increase the heat and foster growth, and at the same time keep undesirable elements at bay. Definition of its application to information technology technology tends to be coloured by the attitude (often negatice) of writers towards it. It occurs in the Wikipedia entry for “closed platform”, for example, but this is prefaced by disclaimer. However, the entry will serve here:

A closed platform, walled garden, or closed ecosystem is a software system wherein the carrier or service provider has control over applications, content, and/or media, and restricts convenient access to non-approved applicants or content.

As an example of its use I reference a piece by John Thornhill, the (US) tech correspondent of the most reputable British newspaper, The Financial Times (March 18, 2021), which had the headline:

Apple’s move to increase privacy strengthens its walled garden

I will not quote the article, but it appears to be free to view for anyone wishing a more extensive explanation.