The sensible approach is to get an Android TV device that you have more control over. You basically have the same freedom with it as with an Android phone or tablet. Plug it into the TV and use the TV only as a monitor/speaker.

Warning: Do not buy cheap Chinese off-brand Android TVs from drop-shipping hellholes like Amazon. These commonly come with malware from the factory. Invest in a quality device with the features that you need.

If you're on a budget, it's possible to make do with a Fire TV Stick, which are often on sale for next to nothing - just don't expect blistering performance or a good UI. They are still Android underneath that awful UI though. You have to fight Amazon's attempts at funneling you towards their own content, but it's doable.

If you want a device that you can easily use for a long time without having to worry about it getting obsolete, get an Nvidia Shield TV or Shield TV Pro. Pricey, but - in my eyes - worth it. At first glance, these may look like every other streaming box, but they justify their relatively high asking prices. For starters, the support for these devices is astonishing, with even the first generation from 2015 still receiving updates. While the current hardware generation is from 2019, it has features you can't get anywhere else, like for example real-time AI upscaling of low-res content in certain apps and (on the Pro model) the ability to serve as a media server instead of just a client:

Hook a storage device up to it (or mount your NAS), add media to them (digitize your home media collection or acquire media from other sources), and use the Plex server application to turn this tiny thing into your own private Netflix that never sees anything delisted. It has enough power to allow you to watch video locally and, at the same time, transcode (=turn media into a format the other device can handle in real-time) up to two more videos (depending on the video files) for other devices in and outside of your home network. This means you could watch something on your TV and at least one other person could watch content you have curated (they don't need a Shield TV - Plex clients are on a wide variety of devices). Given that this is a device that fits into the palm of your hand and needs less than 10W, that's quite astonishing.